JEE Main & Advanced Mathematics Definite Integration Question Bank

done Fundamental definite integration, Definite integration by substitution Total Questions - 110

• question_answer1)
  \[\int_{0}^{1}{{{e}^{2\,\text{In}\,x}}\,dx}=\]                                                                                                         [MP PET 1990]
  A)
                  0 done clear
  B)
                  \[\frac{1}{2}\] done clear
  C)
                  \[\frac{1}{3}\] done clear
  D)
                  \[\frac{1}{4}\] done clear
  View Solution play_arrow

• question_answer2)
  \[\int_{0}^{\pi /4}{{{\tan }^{2}}x\,dx=}\]               [Roorkee 1983, Pb. CET 2000]
  A)
                  \[1-\frac{\pi }{4}\] done clear
  B)
                  \[1+\frac{\pi }{4}\] done clear
  C)
                  \[\frac{\pi }{4}-1\] done clear
  D)
                  \[\frac{\pi }{4}\] done clear
  View Solution play_arrow

• question_answer3)
  \[\int_{0}^{\pi /2}{\frac{x+\sin x}{1+\cos x}\,dx=}\]                                              [MP PET 1989]
  A)
                  \[-\log 2\] done clear
  B)
                  \[\log 2\] done clear
  C)
                  \[\frac{\pi }{2}\] done clear
  D)
                  0 done clear
  View Solution play_arrow

• question_answer4)
  \[\int_{0}^{\pi /2}{{{e}^{x}}\sin x\,dx=}\]                                              [Roorkee 1978]
  A)
                  \[\frac{1}{2}({{e}^{\pi /2}}-1)\] done clear
  B)
                  \[\frac{1}{2}({{e}^{\pi /2}}+1)\] done clear
  C)
                  \[\frac{1}{2}(1-{{e}^{\pi /2}})\] done clear
  D)
                  \[2({{e}^{\pi /2}}+1)\] done clear
  View Solution play_arrow

• question_answer5)
  \[\int_{1}^{2}{{{e}^{x}}\left( \frac{1}{x}-\frac{1}{{{x}^{2}}} \right)\,dx=}\] [MNR 1990; AMU 1999; UPSEAT 2000; Pb. CET 2004]
  A)
                  \[\frac{{{e}^{2}}}{2}+e\] done clear
  B)
                  \[e-\frac{{{e}^{2}}}{2}\] done clear
  C)
                  \[\frac{{{e}^{2}}}{2}-e\] done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer6)
  \[\int_{0}^{\pi /2}{\frac{\cos x}{(1+\sin x)(2+\sin x)}}\,dx=\]                                 [UPSEAT 1999]
  A)
                  \[\log \frac{4}{3}\] done clear
  B)
                  \[\log \frac{1}{3}\] done clear
  C)
                  \[\log \frac{3}{4}\] done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer7)
  \[\int_{\pi /3}^{\pi /2}{\frac{\sqrt{1+\cos x}}{{{(1-\cos x)}^{\frac{5}{2}}}}}\,dx=\]                                             [AI CBSE 1980]
  A)
                  \[\frac{5}{2}\] done clear
  B)
                  \[\frac{3}{2}\] done clear
  C)
                  \[\frac{1}{2}\] done clear
  D)
                  \[\frac{2}{5}\] done clear
  View Solution play_arrow

• question_answer8)
  \[\int_{1}^{2}{\frac{1}{{{x}^{2}}}{{e}^{\frac{-1}{x}}}\,dx=}\]                                 [DCE 2001]
  A)
                  \[\sqrt{e}+1\] done clear
  B)
                  \[\sqrt{e}-1\] done clear
  C)
                  \[\frac{\sqrt{e}+1}{e}\] done clear
  D)
                  \[\frac{\sqrt{e}-1}{e}\] done clear
  View Solution play_arrow

• question_answer9)
  \[\int_{0}^{1}{{{\sin }^{-1}}\left( \frac{2x}{1+{{x}^{2}}} \right)\,dx=}\]                    [Karnataka CET 1999]
  A)
                  \[\frac{\pi }{2}-2\log \sqrt{2}\] done clear
  B)
                  \[\frac{\pi }{2}+2\log \sqrt{2}\] done clear
  C)
                  \[\frac{\pi }{4}-\log \sqrt{2}\] done clear
  D)
                  \[\frac{\pi }{4}+\log \sqrt{2}\] done clear
  View Solution play_arrow

• question_answer10)
  \[\int_{1}^{e}{\frac{{{e}^{x}}}{x}(1+x\log x)\,dx}=\]
  A)
                  \[{{e}^{e}}\] done clear
  B)
                  \[{{e}^{e}}-e\] done clear
  C)
                  \[{{e}^{e}}+e\] done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer11)
  The value of \[\int_{-2}^{2}{(a{{x}^{3}}+bx+c)}\] depends on                 [MNR 1988; UPSEAT 2000]
  A)
                  The value of \[a\]            done clear
  B)
                  The value of \[b\] done clear
  C)
                  The value of \[c\]             done clear
  D)
                  The values of \[a\] and \[b\] done clear
  View Solution play_arrow

• question_answer12)
  \[\int_{\pi /6}^{\pi /4}{\text{cosec}\,2x\,dx=}\]                                                [MNR 1980]
  A)
                  \[\log 3\]             done clear
  B)
                  \[\log \sqrt{3}\] done clear
  C)
                  \[\log 9\]             done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer13)
  \[\int_{0}^{\pi /2}{\sqrt{\cos \theta }{{\sin }^{3}}\theta }\,d\theta =\]
  A)
                  \[\frac{20}{21}\]               done clear
  B)
                  \[\frac{8}{21}\] done clear
  C)
                  \[\frac{-20}{21}\]             done clear
  D)
                  \[\frac{-8}{21}\] done clear
  View Solution play_arrow

• question_answer14)
  \[\int_{0}^{\pi /4}{{{\sec }^{7}}\theta {{\sin }^{3}}\theta }\,d\theta =\]
  A)
                  \[\frac{1}{12}\] done clear
  B)
                  \[\frac{3}{12}\] done clear
  C)
                  \[\frac{5}{12}\] done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer15)
  \[\int_{a}^{b}{\frac{\log x}{x}\,dx=}\]                                    [MP PET 1994]
  A)
                  \[\log \left( \frac{\log b}{\log a} \right)\]               done clear
  B)
                  \[\log (a\,b)\log \,\left( \frac{b}{a} \right)\] done clear
  C)
                  \[\frac{1}{2}\log (a\,b)\log \,\left( \frac{b}{a} \right)\]    done clear
  D)
                  \[\frac{1}{2}\log (a\,b)\log \,\left( \frac{a}{b} \right)\] done clear
  View Solution play_arrow

• question_answer16)
  \[\int_{0}^{1}{{{\tan }^{-1}}x\,dx=}\]     [Karnataka CET 1993; RPET 1997]
  A)
                  \[\frac{\pi }{4}-\frac{1}{2}\log 2\]             done clear
  B)
                  \[\pi -\frac{1}{2}\log 2\] done clear
  C)
                  \[\frac{\pi }{4}-\log 2\]  done clear
  D)
                  \[\pi -\log 2\] done clear
  View Solution play_arrow

• question_answer17)
  \[\int_{0}^{1}{\frac{dx}{{{[ax+b(1-x)]}^{2}}}}=\]                                     [SCRA 1986]
  A)
                  \[\frac{a}{b}\]   done clear
  B)
                  \[\frac{b}{a}\] done clear
  C)
                  \[a\,b\] done clear
  D)
                  \[\frac{1}{a\,b}\] done clear
  View Solution play_arrow

• question_answer18)
  If \[\int_{0}^{k}{\frac{dx}{2+8{{x}^{2}}}}=\frac{\pi }{16}\,,\] then \[k=\]
  A)
                  1              done clear
  B)
                  \[\frac{1}{2}\] done clear
  C)
                  \[\frac{1}{4}\]    done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer19)
  \[\int_{\pi /4}^{\pi /2}{\cos \theta \,\text{cose}{{\text{c}}^{\text{2}}}\theta \,d\theta =}\]                                         [Roorkee 1978]
  A)
                  \[\sqrt{2}-1\]     done clear
  B)
                  \[1-\sqrt{2}\] done clear
  C)
                  \[\sqrt{2}+1\]    done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer20)
  \[\int_{0}^{1/\sqrt{2}}{\frac{{{\sin }^{-1}}x}{{{(1-{{x}^{2}})}^{3/2}}}dx=}\]                                            [Roorkee 1984]
  A)
                  \[\frac{\pi }{4}+\frac{1}{2}\log 2\]            done clear
  B)
                  \[\frac{\pi }{4}-\frac{1}{2}\log 2\] done clear
  C)
                  \[\frac{\pi }{2}+\log 2\] done clear
  D)
                  \[\frac{\pi }{2}-\log 2\] done clear
  View Solution play_arrow

• question_answer21)
  The correct evaluation of \[\int_{0}^{\pi /2}{\sin x\,\sin 2x}\] is [MP PET 1993, 2003]
  A)
                  \[\frac{4}{3}\]    done clear
  B)
                  \[\frac{1}{3}\] done clear
  C)
                  \[\frac{3}{4}\]    done clear
  D)
                  \[\frac{2}{3}\] done clear
  View Solution play_arrow

• question_answer22)
  \[\int_{0}^{\pi /2}{\frac{dx}{2+\cos x}}=\]                                             [BIT Ranchi 1992]
  A)
                  \[\frac{1}{\sqrt{3}}{{\tan }^{-1}}\left( \frac{1}{\sqrt{3}} \right)\]                done clear
  B)
                  \[\sqrt{3}{{\tan }^{-1}}\left( \sqrt{3} \right)\] done clear
  C)
                  \[\frac{2}{\sqrt{3}}{{\tan }^{-1}}\left( \frac{1}{\sqrt{3}} \right)\]                done clear
  D)
                  \[2\sqrt{3}{{\tan }^{-1}}\left( \sqrt{3} \right)\] done clear
  View Solution play_arrow

• question_answer23)
  \[\int_{0}^{1}{\frac{{{\tan }^{-1}}x}{1+{{x}^{2}}}}\,dx=\]             [SCRA 1987; MNR 1990]
  A)
                  \[\frac{{{\pi }^{2}}}{8}\] done clear
  B)
                  \[\frac{{{\pi }^{2}}}{16}\] done clear
  C)
                  \[\frac{{{\pi }^{2}}}{4}\] done clear
  D)
                  \[\frac{{{\pi }^{2}}}{32}\] done clear
  View Solution play_arrow

• question_answer24)
  \[\int_{1}^{2}{\frac{\cos (\log x)}{x}}\,dx=\]
  A)
                  \[\sin \,(\log 3)\]              done clear
  B)
                  \[\sin \,(\log 2)\] done clear
  C)
                  \[\cos \,(\log 3)\]             done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer25)
  \[\int_{0}^{a}{\frac{x\,dx}{\sqrt{{{a}^{2}}+{{x}^{2}}}}}=\]
  A)
                  \[a\,(\sqrt{2}-1)\]            done clear
  B)
                  \[a\,(1-\sqrt{2})\] done clear
  C)
                  \[a\,(1+\sqrt{2})\]           done clear
  D)
                  \[2a\sqrt{3}\] done clear
  View Solution play_arrow

• question_answer26)
  The value of integral \[\int_{1/\pi }^{2/\pi }{\frac{\sin (1/x)}{{{x}^{2}}}}\,dx=\]  [IIT 1990]
  A)
                  2              done clear
  B)
                  \[-1\] done clear
  C)
                  0              done clear
  D)
                  1 done clear
  View Solution play_arrow

• question_answer27)
  \[\int_{0}^{a}{\frac{{{x}^{4}}\,dx}{{{({{a}^{2}}+{{x}^{2}})}^{4}}}}=\]
  A)
                  \[\frac{1}{16{{a}^{3}}}\left( \frac{\pi }{4}-\frac{1}{3} \right)\]      done clear
  B)
                  \[\frac{1}{16{{a}^{3}}}\left( \frac{\pi }{4}+\frac{1}{3} \right)\] done clear
  C)
                  \[\frac{1}{16}{{a}^{3}}\left( \frac{\pi }{4}-\frac{1}{3} \right)\]      done clear
  D)
                  \[\frac{1}{16}{{a}^{3}}\left( \frac{\pi }{4}+\frac{1}{3} \right)\] done clear
  View Solution play_arrow

• question_answer28)
  \[\int_{0}^{2\pi }{{{e}^{x/2}}.\sin \left( \frac{x}{2}+\frac{\pi }{4} \right)\,dx=}\]                                 [Roorkee 1982]
  A)
                  1              done clear
  B)
                  \[2\sqrt{2}\] done clear
  C)
                  0              done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer29)
  \[\int_{0}^{1}{\frac{{{e}^{-x}}}{1+{{e}^{-x}}}}\,dx=\]                                             [Roorkee 1976]
  A)
                  \[\log \left( \frac{1+e}{e} \right)-\frac{1}{e}+1\]               done clear
  B)
                  \[\log \left( \frac{1+e}{2e} \right)-\frac{1}{e}+1\] done clear
  C)
                  \[\log \left( \frac{1+e}{2e} \right)+\frac{1}{e}-1\]             done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer30)
   \[\int_{0}^{\pi /4}{\frac{\sin x+\cos x}{9+16\sin 2x}\,dx=}\]                                        [IIT 1983]
  A)
                  \[\frac{1}{20}\log 3\]      done clear
  B)
                  \[\log 3\] done clear
  C)
                  \[\frac{1}{20}\log 5\] done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer31)
   \[\int_{\pi \text{/4}}^{\pi \text{/2}}{{{e}^{x}}(\log \sin x+\cot x)\,dx=}\]                                             [AI CBSE 1991]
  A)
                  \[{{e}^{\pi /4}}\log 2\]   done clear
  B)
                  \[-{{e}^{\pi /4}}\log 2\] done clear
  C)
                  \[\frac{1}{2}{{e}^{\pi /4}}\log 2\]              done clear
  D)
                  \[-\frac{1}{2}{{e}^{\pi /4}}\log 2\] done clear
  View Solution play_arrow

• question_answer32)
   \[\int_{0}^{1/2}{\frac{x{{\sin }^{-1}}x}{\sqrt{1-{{x}^{2}}}}\,dx=}\]                                            [IIT 1984]
  A)
                  \[\frac{1}{2}+\frac{\sqrt{3}\pi }{12}\]      done clear
  B)
                  \[\frac{1}{2}-\frac{\sqrt{3}\pi }{12}\] done clear
  C)
                  \[\frac{1}{2}-\frac{\sqrt{3\pi }}{12}\]       done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer33)
   \[\int_{0}^{2}{\sqrt{\frac{2+x}{2-x}}}\,dx=\]                                      [MNR 1984; CEE 1993]
  A)
                  \[\pi +2\]             done clear
  B)
                  \[\pi +\frac{3}{2}\] done clear
  C)
                  \[\pi +1\]             done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer34)
   \[\int_{0}^{\pi }{\frac{dx}{1+\sin x}}=\]                                                [CEE 1993]
  A)
                  0              done clear
  B)
                  \[\frac{1}{2}\] done clear
  C)
                  2              done clear
  D)
                  \[\frac{3}{2}\] done clear
  View Solution play_arrow

• question_answer35)
  \[\int_{0}^{\pi /8}{\frac{{{\sec }^{2}}2x}{2}\,dx=}\]
  A)
                  \[\frac{1}{4}\]    done clear
  B)
                  \[\frac{1}{3}\] done clear
  C)
                  \[\frac{1}{2}\]    done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer36)
  \[\int_{0}^{2\pi }{\sqrt{1+\sin \frac{x}{2}}\,dx=}\]            [MNR 1987; UPSEAT 2000]
  A)
                  0              done clear
  B)
                  2 done clear
  C)
                  8              done clear
  D)
                  4 done clear
  View Solution play_arrow

• question_answer37)
  \[\int_{0}^{1}{{{\cos }^{-1}}x\,dx=}\]                                      [DSSE 1988]
  A)
                  0              done clear
  B)
                  1 done clear
  C)
                  2              done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer38)
  \[\int_{0}^{\pi /2}{\frac{\cos x}{1+\cos x+\sin x}}\,dx=\]                                               [Roorkee 1989]
  A)
                  \[\frac{\pi }{4}+\frac{1}{2}\log 2\]            done clear
  B)
                  \[\frac{\pi }{4}+\log 2\] done clear
  C)
                  \[\frac{\pi }{4}-\frac{1}{2}\log 2\]             done clear
  D)
                  \[\frac{\pi }{4}-\log 2\] done clear
  View Solution play_arrow

• question_answer39)
  \[\int_{0}^{\pi /6}{(2+3{{x}^{2}})\cos 3x\,dx=}\]                                               [DSSE 1985]
  A)
                  \[\frac{1}{36}(\pi +16)\]                done clear
  B)
                  \[\frac{1}{36}(\pi -16)\] done clear
  C)
                  \[\frac{1}{36}({{\pi }^{2}}-16)\]  done clear
  D)
                  \[\frac{1}{36}({{\pi }^{2}}+16)\] done clear
  View Solution play_arrow

• question_answer40)
  \[\int_{0}^{\pi /2}{\frac{\sin x\cos x}{1+{{\sin }^{4}}x}\,dx=}\]                                   [AISSE 1988]
  A)
                  \[\frac{\pi }{2}\]               done clear
  B)
                  \[\frac{\pi }{4}\] done clear
  C)
                  \[\frac{\pi }{6}\]               done clear
  D)
                  \[\frac{\pi }{8}\] done clear
  View Solution play_arrow

• question_answer41)
  \[\int_{0}^{\pi /4}{{{\tan }^{6}}x{{\sec }^{2}}x\,dx=}\]                                    [BIT Ranchi 1981]
  A)
                  \[\frac{1}{7}\]    done clear
  B)
                  \[\frac{2}{7}\] done clear
  C)
                  1              done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer42)
  \[\int_{0}^{2}{\frac{{{x}^{3}}\,dx}{{{({{x}^{2}}+1)}^{\frac{3}{2}}}}}=\]
  A)
                  \[{{(\sqrt{2}-1)}^{2}}\]   done clear
  B)
                  \[\frac{{{(\sqrt{2}-1)}^{2}}}{\sqrt{2}}\] done clear
  C)
                  \[\frac{\sqrt{2}-1}{\sqrt{2}}\]     done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer43)
   \[\int_{0}^{\pi /6}{\frac{\sin x}{{{\cos }^{3}}x}\,dx=}\]                                  [SCRA 1979]
  A)
                  \[\frac{2}{3}\]    done clear
  B)
                  \[\frac{1}{6}\] done clear
  C)
                  2              done clear
  D)
                  \[\frac{1}{3}\] done clear
  View Solution play_arrow

• question_answer44)
  \[\int_{0}^{\pi /2}{\frac{\sin x\cos x\,dx}{{{\cos }^{2}}x+3\cos x+2}}=\]                                 [MNR 1981]
  A)
                  \[\log \left( \frac{8}{9} \right)\] done clear
  B)
                  \[\log \left( \frac{9}{8} \right)\] done clear
  C)
                  \[\log (8\times 9)\]         done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer45)
  The value of the integral \[\int_{0}^{\log 5}{\frac{{{e}^{x}}\sqrt{{{e}^{x}}-1}}{{{e}^{x}}+3}}\,dx=\]
  A)
                  \[3+2\pi \]           done clear
  B)
                  \[4-\pi \] done clear
  C)
                  \[2+\pi \]             done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer46)
  The value of the definite integral \[\int_{0}^{1}{\frac{dx}{{{x}^{2}}+2x\cos \alpha +1}}\] for \[0<\alpha <\pi \] is equal to [Kurukshetra CEE 2002]
  A)
                  \[\sin \alpha \]  done clear
  B)
                  \[{{\tan }^{-1}}(\sin \alpha )\] done clear
  C)
                  \[\alpha \sin \alpha \]    done clear
  D)
                  \[\frac{\alpha }{2}{{(\sin \alpha )}^{-1}}\] done clear
  View Solution play_arrow

• question_answer47)
  The value of the integral \[\int_{-\pi }^{\pi }{\sin mx\sin nx\,dx}\] for \[m\ne n\] \[(m,\,\,n\in I),\] is
  A)
                  0              done clear
  B)
                  \[\pi \] done clear
  C)
                  \[\frac{\pi }{2}\]               done clear
  D)
                  \[2\pi \] done clear
  View Solution play_arrow

• question_answer48)
  The greater of \[\int_{0}^{\pi /2}{\frac{\sin x}{x}\,dx}\] and \[\frac{\pi }{2},\] is
  A)
                  \[\frac{\pi }{2}\]               done clear
  B)
                  \[\int_{0}^{\pi /2}{\frac{\sin x}{x}\,dx}\] done clear
  C)
                  Nothing can be said        done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer49)
  The integral \[\int_{-1}^{3}{\left( {{\tan }^{-1}}\frac{x}{{{x}^{2}}+1}+{{\tan }^{-1}}\frac{{{x}^{2}}+1}{x} \right)}\,dx=\]                                                                 [Karnataka CET 2000]
  A)
                  \[\pi \]  done clear
  B)
                  \[2\pi \] done clear
  C)
                  \[3\pi \]                done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer50)
  If \[{{I}_{1}}=\int_{e}^{{{e}^{2}}}{\frac{dx}{\log x}}\] and \[{{I}_{2}}=\int_{1}^{2}{\frac{{{e}^{x}}}{x}\,dx,}\] then                                                                 [Karnataka CET 2000]
  A)
                  \[{{I}_{1}}={{I}_{2}}\]     done clear
  B)
                  \[{{I}_{1}}>{{I}_{2}}\] done clear
  C)
                  \[{{I}_{1}}<{{I}_{2}}\]     done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer51)
  \[\int_{-\pi /4}^{\pi /2}{{{e}^{-x}}\sin x\,dx}=\]                                 [CEE 1993]
  A)
                  \[-\frac{1}{2}{{e}^{-\pi /2}}\]      done clear
  B)
                  \[-\frac{\sqrt{2}}{2}{{e}^{-\pi /4}}\] done clear
  C)
                  \[-\sqrt{2}({{e}^{-\pi /4}}+{{e}^{-\pi /4}})\]         done clear
  D)
                  0 done clear
  View Solution play_arrow

• question_answer52)
  \[\int_{0}^{\pi /2}{\frac{1+2\cos x}{{{(2+\cos x)}^{2}}}=}\]                                           [CEE 1993]
  A)
                  \[\frac{\pi }{2}\]               done clear
  B)
                  \[\pi \] done clear
  C)
                  \[\frac{1}{2}\]    done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer53)
  \[\int_{0}^{\pi }{\frac{dx}{1-2a\cos x+{{a}^{2}}}}\,\]=                                     [CEE 1993]
  A)
                  \[\frac{\pi }{2(1-{{a}^{2}})}\]       done clear
  B)
                  \[\pi (1-{{a}^{2}})\] done clear
  C)
                  \[\frac{\pi }{1-{{a}^{2}}}\]            done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer54)
  \[\int_{0}^{1}{{{(1-x)}^{9}}dx=}\]                                             [SCRA 1979]
  A)
                  1              done clear
  B)
                  \[\frac{1}{10}\] done clear
  C)
                  \[\frac{11}{10}\]               done clear
  D)
                  2 done clear
  View Solution play_arrow

• question_answer55)
  \[\int_{0}^{\pi /3}{\cos 3x\,dx=}\]                                           [SCRA 1980]
  A)
                  \[\pi \]  done clear
  B)
                  0 done clear
  C)
                  \[\frac{\pi }{2}\]               done clear
  D)
                  \[\frac{\pi }{4}\] done clear
  View Solution play_arrow

• question_answer56)
  The value of \[\int_{0}^{\pi /4}{\frac{1+\tan x}{1-\tan x}\,dx}\] is                             [SCRA 1986]
  A)
                  \[-\frac{1}{2}\log 2\]       done clear
  B)
                  \[\frac{1}{4}\log 2\] done clear
  C)
                  \[\frac{1}{3}\log 2\]        done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer57)
  The value of \[\int_{0}^{1}{\frac{dx}{{{e}^{x}}+{{e}^{-x}}}}\] is                                  [SCRA 1980]
  A)
                  \[{{\tan }^{-1}}\left( \frac{1-e}{1+e} \right)\]      done clear
  B)
                  \[{{\tan }^{-1}}\left( \frac{e-1}{e+1} \right)\] done clear
  C)
                  \[\frac{\pi }{4}\]               done clear
  D)
                  \[{{\tan }^{-1}}e+\frac{\pi }{4}\] done clear
  View Solution play_arrow

• question_answer58)
  \[\int_{1}^{e}{\frac{1+\log x}{x}\,dx=}\]                                               [SCRA 1986]
  A)
                  \[\frac{3}{2}\]    done clear
  B)
                  \[\frac{1}{2}\] done clear
  C)
                  \[\frac{1}{e}\]   done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer59)
  If \[\int_{0}^{1}{x\log \left( 1+\frac{x}{2} \right)}\,dx=a+b\log \frac{2}{3},\] then              [SCRA 1986]
  A)
                  \[a=\frac{3}{2},\,\,\,b=\frac{3}{2}\]         done clear
  B)
                  \[a=\frac{3}{4},\,\,\,b=-\frac{3}{4}\] done clear
  C)
                  \[a=\frac{3}{4},\,\,\,b=\frac{3}{2}\]         done clear
  D)
                  \[a=b\] done clear
  View Solution play_arrow

• question_answer60)
  \[\int_{0}^{1}{\frac{dx}{\sqrt{1+x}-\sqrt{x}}=}\]                                               [SCRA 1986]
  A)
                  \[\frac{2\sqrt{2}}{3}\]    done clear
  B)
                  \[\frac{4\sqrt{2}}{3}\] done clear
  C)
                  \[\frac{8\sqrt{2}}{3}\]    done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer61)
  \[\int_{0}^{\pi /4}{\frac{4\sin 2\theta \,d\theta }{{{\sin }^{4}}\theta +{{\cos }^{4}}\theta }}=\]                                   [SCRA 1986]
  A)
                  \[\pi /4\]              done clear
  B)
                  \[\pi /2\] done clear
  C)
                  \[\pi \]  done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer62)
  \[\int_{0}^{1}{\frac{{{e}^{x}}(x-1)}{{{(x+1)}^{3}}}\,dx=}\]                                             [SCRA 1986]
  A)
                  \[\frac{e}{4}\]   done clear
  B)
                  \[\frac{e}{4}-1\] done clear
  C)
                  \[\frac{e}{4}+1\]              done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer63)
  If \[x({{x}^{4}}+1)\varphi (x)=1,\] then \[\int_{1}^{2}{\varphi (x)\,dx=}\]              [SCRA 1986]
  A)
                  \[\frac{1}{4}\log \frac{32}{17}\] done clear
  B)
                  \[\frac{1}{2}\log \frac{32}{17}\] done clear
  C)
                  \[\frac{1}{4}\log \frac{16}{17}\] done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer64)
  \[\int_{1/4}^{1/2}{\frac{dx}{\sqrt{x-{{x}^{2}}}}=}\]                                          [SCRA 1986]
  A)
                  \[\pi \]  done clear
  B)
                  \[\frac{\pi }{2}\] done clear
  C)
                  \[\frac{\pi }{3}\]               done clear
  D)
                  \[\frac{\pi }{6}\] done clear
  View Solution play_arrow

• question_answer65)
  The value of \[\int_{0}^{2}{\frac{{{3}^{\sqrt{x}}}}{\sqrt{x}}}\,dx\] is                                        [SCRA 1992]
  A)
                  \[\frac{2}{\log 3}.({{3}^{\sqrt{2}}}-1)\]   done clear
  B)
                  0 done clear
  C)
                  \[2.\frac{\sqrt{2}}{\log 3}\]          done clear
  D)
                  \[\frac{{{3}^{\sqrt{2}}}}{\sqrt{2}}\] done clear
  View Solution play_arrow

• question_answer66)
  \[\int_{0}^{2\pi }{\,\,(\sin x+\cos x)\,dx=}\]                                        [SCRA 1991]
  A)
                  0              done clear
  B)
                  2 done clear
  C)
                  \[-2\]     done clear
  D)
                  1 done clear
  View Solution play_arrow

• question_answer67)
  \[\int_{0}^{\pi /4}{\frac{\sec x}{1+2{{\sin }^{2}}x}}\] is equal to                                 [MNR 1994]
  A)
                  \[\frac{1}{3}\left[ \log (\sqrt{2}+1)+\frac{\pi }{2\sqrt{2}} \right]\]             done clear
  B)
                  \[\frac{1}{3}\left[ \log (\sqrt{2}+1)-\frac{\pi }{2\sqrt{2}} \right]\] done clear
  C)
                  \[3\left[ \log (\sqrt{2}+1)-\frac{\pi }{2\sqrt{2}} \right]\] done clear
  D)
                  \[3\left[ \log (\sqrt{2}+1)+\frac{\pi }{2\sqrt{2}} \right]\] done clear
  View Solution play_arrow

• question_answer68)
  The value of \[\int_{0}^{\pi /2}{\frac{\sin x}{1+{{\cos }^{2}}x}\,dx}\] is                   [RPET 1995]
  A)
                  \[\pi /2\]              done clear
  B)
                  \[\pi /4\] done clear
  C)
                  \[\pi /3\]              done clear
  D)
                  \[\pi /6\] done clear
  View Solution play_arrow

• question_answer69)
  The value of \[\int_{1}^{2}{\log x\,dx}\] is                                            [Roorkee 1995]
  A)
                  \[\log 2/e\]         done clear
  B)
                  \[\log 4\] done clear
  C)
                  \[\log 4/e\]         done clear
  D)
                  \[\log 2\] done clear
  View Solution play_arrow

• question_answer70)
  The value of \[\int_{3}^{5}{\frac{{{x}^{2}}}{{{x}^{2}}-4}\,dx}\] is                                                [Roorkee 1992]
  A)
                  \[2-{{\log }_{e}}\left( \frac{15}{7} \right)\] done clear
  B)
                  \[2+{{\log }_{e}}\left( \frac{15}{7} \right)\] done clear
  C)
                  \[2+4{{\log }_{e}}3-4{{\log }_{e}}7+4{{\log }_{e}}5\] done clear
  D)
                  \[2-{{\tan }^{-1}}\left( \frac{15}{7} \right)\] done clear
  View Solution play_arrow

• question_answer71)
  \[\int_{0}^{\pi /4}{\frac{dx}{{{\cos }^{4}}x-{{\cos }^{2}}x{{\sin }^{2}}x+{{\sin }^{4}}x}=}\]
  A)
                  \[\frac{\pi }{2}\]               done clear
  B)
                  \[\frac{\pi }{4}\] done clear
  C)
                  \[\frac{\pi }{3}\]               done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer72)
  The value of \[\int_{0}^{{{\sin }^{2}}x}{{{\sin }^{-1}}\sqrt{t}\,dt+\int_{0}^{{{\cos }^{2}}x}{{{\cos }^{-1}}\sqrt{t}\,dt}}\] is [MP PET 2001; Orissa JEE 2005]
  A)
                  \[\frac{\pi }{2}\]               done clear
  B)
                  1 done clear
  C)
                  \[\frac{\pi }{4}\]               done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer73)
  If for non-zero \[x,\] \[af(x)+bf\left( \frac{1}{x} \right)=\frac{1}{x}-5,\] where \[a\ne b,\] then \[\int_{1}^{2}{f(x)\,dx=}\]                                           [IIT 1996]
  A)
                  \[\frac{1}{({{a}^{2}}+{{b}^{2}})}\left[ a\log 2-5a+\frac{7}{2}b \right]\] done clear
  B)
                  \[\frac{1}{({{a}^{2}}-{{b}^{2}})}\left[ a\log 2-5a+\frac{7}{2}b \right]\] done clear
  C)
                  \[\frac{1}{({{a}^{2}}-{{b}^{2}})}\left[ a\log 2-5a-\frac{7}{2}b \right]\] done clear
  D)
                  \[\frac{1}{({{a}^{2}}+{{b}^{2}})}\left[ a\log 2-5a-\frac{7}{2}b \right]\] done clear
  View Solution play_arrow

• question_answer74)
  If \[{{I}_{n}}=\int_{0}^{\pi /4}{{{\tan }^{n}}\theta \,d\theta ,}\] then \[{{I}_{8}}+{{I}_{6}}\] equals [Kurukshetra CEE 1996]
  A)
                  \[\frac{1}{4}\]    done clear
  B)
                  \[\frac{1}{5}\] done clear
  C)
                  \[\frac{1}{6}\]    done clear
  D)
                  \[\frac{1}{7}\] done clear
  View Solution play_arrow

• question_answer75)
  \[\int_{0}^{\pi /4}{{}}\sec x\log (\sec x+\tan x)\,dx=\]
  A)
                  \[\frac{1}{2}{{[\log (1+\sqrt{2})]}^{2}}\] done clear
  B)
                  \[{{[\log (1+\sqrt{2})]}^{2}}\] done clear
  C)
                  \[\frac{1}{2}{{[\log (\sqrt{2}-1)]}^{2}}\] done clear
  D)
                  \[\frac{1}{2}{{[\log (\sqrt{2}-1)]}^{2}}\] done clear
  View Solution play_arrow

• question_answer76)
  \[\int_{0}^{\pi /4}{\frac{{{\sec }^{2}}x}{(1+\tan x)(2+\tan x)}}\,dx=\]
  A)
                  \[{{\log }_{e}}\left( \frac{2}{3} \right)\]  done clear
  B)
                  \[{{\log }_{e}}3\] done clear
  C)
                  \[\frac{1}{2}{{\log }_{e}}\left( \frac{4}{3} \right)\]             done clear
  D)
                  \[{{\log }_{e}}\left( \frac{4}{3} \right)\] done clear
  View Solution play_arrow

• question_answer77)
  \[\int_{0}^{2/3}{\frac{dx}{4+9{{x}^{2}}}=}\]                                        [MP PET 1997]
  A)
                  \[\frac{\pi }{12}\]             done clear
  B)
                  \[\frac{\pi }{24}\] done clear
  C)
                  \[\frac{\pi }{4}\]               done clear
  D)
                  0 done clear
  View Solution play_arrow

• question_answer78)
  The value of \[\int_{0}^{1}{\frac{{{x}^{4}}+1}{{{x}^{2}}+1}\,dx}\] is                                          [MP PET 1998]
  A)
                  \[\frac{1}{6}(3\pi -4)\]   done clear
  B)
                  \[\frac{1}{6}(3-4\pi )\] done clear
  C)
                  \[\frac{1}{6}(3\pi +4)\]  done clear
  D)
                  \[\frac{1}{6}(3+4\pi )\] done clear
  View Solution play_arrow

• question_answer79)
  \[\int_{0}^{a}{{{x}^{2}}\sin {{x}^{3}}\,dx}\] equals                                           [RPET 1996]
  A)
                  \[(1-\cos {{a}^{3}})\]      done clear
  B)
                  \[3(1-\cos {{a}^{3}})\] done clear
  C)
                  \[-\frac{1}{3}(1-\cos {{a}^{3}})\]                done clear
  D)
                  \[\frac{1}{3}(1-\cos {{a}^{3}})\] done clear
  View Solution play_arrow

• question_answer80)
  \[\int_{0}^{\pi /4}{[\sqrt{\tan x}+\sqrt{\cot x}]\,dx}\] equals                      [RPET 1997]
  A)
                  \[\sqrt{2}\pi \]  done clear
  B)
                  \[\frac{\pi }{2}\] done clear
  C)
                  \[\frac{\pi }{\sqrt{2}}\]  done clear
  D)
                  \[2\pi \] done clear
  View Solution play_arrow

• question_answer81)
  \[\int_{0}^{1}{\sqrt{\frac{1-x}{1+x}}}\,dx\] equals          [RPET 1997; IIT Screening 2004]
  A)
                  \[\left( \frac{\pi }{2}-1 \right)\]  done clear
  B)
                  \[\left( \frac{\pi }{2}+1 \right)\] done clear
  C)
                  \[\frac{\pi }{2}\]               done clear
  D)
                  \[(\pi +1)\] done clear
  View Solution play_arrow

• question_answer82)
  \[\int_{1}^{e}{\frac{1}{x}\,dx}\] is equals to        [SCRA 1996; Pb. CET 2003]
  A)
                  \[\infty \]            done clear
  B)
                  0 done clear
  C)
                  1              done clear
  D)
                  \[\log (1+e)\] done clear
  View Solution play_arrow

• question_answer83)
  \[\int_{\,1}^{\,x}{\frac{\log {{x}^{2}}}{x}\,dx=}\]                                               [DCE 1999]
  A)
                  \[{{(\log x)}^{2}}\]           done clear
  B)
                  \[\frac{1}{2}{{(\log x)}^{2}}\] done clear
  C)
                  \[\frac{\log {{x}^{2}}}{2}\]            done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer84)
  \[\frac{1}{2}(e-3)\]          [SCRA 1986; Karnataka CET 1999]
  A)
                  \[\pi ab\]             done clear
  B)
                  \[{{\pi }^{2}}ab\] done clear
  C)
                  \[\frac{\pi }{ab}\]             done clear
  D)
                  \[\frac{\pi }{2ab}\] done clear
  View Solution play_arrow

• question_answer85)
  \[\int_{0}^{\pi /4}{{}}(\cos x-\sin x)dx+\int_{\pi /4}^{5\pi /4}{{}}(\sin x-\cos x)dx\]                    \[+\int_{2\pi }^{\pi /4}{{}}(\cos x-\sin x)\,dx\] is equal to              [RPET 2000]
  A)
                  \[\sqrt{2}-2\]     done clear
  B)
                  \[2\sqrt{2}-2\] done clear
  C)
                  \[3\sqrt{2}-2\]   done clear
  D)
                  \[4\sqrt{2}-2\] done clear
  View Solution play_arrow

• question_answer86)
  \[\left( \int_{\,0}^{\,a}{x\,dx} \right)\le (a+4),\] then                                     [RPET 2000]
  A)
                  \[\frac{24}{5}\pi \]           done clear
  B)
                  \[-2\le a\le 4\] done clear
  C)
                  \[-2\le a\le 0\]   done clear
  D)
                  \[a\le -2\,\,\text{or}\,\,a\ge 4\] done clear
  View Solution play_arrow

• question_answer87)
  The value of \[\int_{\,-\,1}^{\,3}{\,{{\tan }^{-1}}\left( \frac{x}{{{x}^{2}}+1} \right)+{{\tan }^{-1}}\left( \frac{{{x}^{2}}+1}{x} \right)\,dx}\] is                 [Karnataka CET 2000]
  A)
                  \[2\pi \]                done clear
  B)
                  \[\pi \] done clear
  C)
                  \[\frac{21}{5}\pi \]           done clear
  D)
                  \[\frac{\pi }{4}\] done clear
  View Solution play_arrow

• question_answer88)
  \[\int_{\,-\,1}^{\,0}{\frac{dx}{{{x}^{2}}+2x+2}=}\]                                 [MP PET 2000]
  A)
                  0              done clear
  B)
                  \[\pi /4\] done clear
  C)
                  \[\pi /2\]              done clear
  D)
                  \[-\pi /4\] done clear
  View Solution play_arrow

• question_answer89)
  The value of \[\int_{\,0}^{\,1}{\frac{{{\tan }^{-1}}x}{1+{{x}^{2}}}dx}\] is                               [RPET 2001]
  A)
                  \[\pi /4\]              done clear
  B)
                  \[{{\pi }^{2}}/32\] done clear
  C)
                  1              done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer90)
  \[\int_{1}^{\sqrt{3}}{\frac{1}{1+{{x}^{2}}}dx}\] is equal to                                            [DCE 2002]
  A)
                  \[\pi /12\]           done clear
  B)
                  \[\pi /6\] done clear
  C)
                  \[\pi /4\]              done clear
  D)
                  \[\pi /3\] done clear
  View Solution play_arrow

• question_answer91)
  \[\int_{\,1}^{\,3}{(x-1)(x-2)(x-3)dx=}\]                                  [Karnataka CET 2002]
  A)
                  3              done clear
  B)
                  2 done clear
  C)
                  1              done clear
  D)
                  0 done clear
  View Solution play_arrow

• question_answer92)
  \[\int_{\,2}^{\,3}{\frac{dx}{{{x}^{2}}-x}=}\]                                         [EAMCET 2002]
  A)
                  \[\log (2/3)\]      done clear
  B)
                  \[\log (1/4)\] done clear
  C)
                  \[\log (4/3)\]      done clear
  D)
                  \[\log (8/3)\] done clear
  View Solution play_arrow

• question_answer93)
  \[\int_{\,8}^{\,15}{\frac{dx}{(x-3)\sqrt{x+1}}=}\]                                              [UPSEAT 2003]
  A)
                  \[\frac{1}{2}\log \frac{5}{3}\]      done clear
  B)
                  \[\frac{1}{3}\log \frac{5}{3}\] done clear
  C)
                  \[\frac{1}{2}\log \frac{3}{5}\]      done clear
  D)
                  \[\frac{1}{5}\log \frac{3}{5}\] done clear
  View Solution play_arrow

• question_answer94)
  The value of \[\int_{\,0}^{\,\pi }{\,\left| \,{{\sin }^{3}}\theta \, \right|\,d\theta }\] is                      [UPSEAT 2003]
  A)
                  0              done clear
  B)
                  3/8 done clear
  C)
                  4/3         done clear
  D)
                  \[\pi \] done clear
  View Solution play_arrow

• question_answer95)
  \[\int_{\,0}^{\,1}{\,\sin \left( 2{{\tan }^{-1}}\sqrt{\frac{1+x}{1-x}} \right)\,dx=}\]                                              [EAMCET 2003]
  A)
                  \[\pi /6\]              done clear
  B)
                  \[\pi /4\] done clear
  C)
                  \[\pi /2\]              done clear
  D)
                  \[\pi \] done clear
  View Solution play_arrow

• question_answer96)
  \[\int_{\,0}^{\,3}{\,\frac{3x+1}{{{x}^{2}}+9}dx=}\]                                           [EAMCET 2003]
  A)
                  \[\log (2\sqrt{2})+\frac{\pi }{12}\]            done clear
  B)
                  \[\log (2\sqrt{2})+\frac{\pi }{2}\] done clear
  C)
                  \[\log (2\sqrt{2})+\frac{\pi }{6}\]              done clear
  D)
                  \[\log (2\sqrt{2})+\frac{\pi }{3}\] done clear
  View Solution play_arrow

• question_answer97)
  The value of \[\int_{1}^{2}{\frac{dx}{x(1+{{x}^{4}})}}\]is                                               [MP PET 2004]
  A)
                  \[\frac{1}{4}\log \frac{17}{32}\] done clear
  B)
                  \[\frac{1}{4}\log \frac{17}{2}\] done clear
  C)
                  \[\log \frac{17}{2}\]        done clear
  D)
                  \[\frac{1}{4}\log \frac{32}{17}\] done clear
  View Solution play_arrow

• question_answer98)
  The value of\[\int_{2}^{3}{\frac{x+1}{{{x}^{2}}(x-1)}dx}\]is                                          [MP PET 2004]
  A)
                  \[2\log 2-\frac{1}{6}\]    done clear
  B)
                  \[\log \frac{16}{9}-\frac{1}{6}\] done clear
  C)
                  \[\log \frac{4}{3}-\frac{1}{6}\]    done clear
  D)
                  \[\log \frac{16}{9}+\frac{1}{6}\] done clear
  View Solution play_arrow

• question_answer99)
  The value of \[\int_{1}^{e}{\log x\,dx}\]is                                            [Pb. CET 2001]
  A)
                  \[0\]      done clear
  B)
                  1 done clear
  C)
                  \[e-1\]  done clear
  D)
                  \[e+1\] done clear
  View Solution play_arrow

• question_answer100)
  The value of \[I=\int_{0}^{\pi /2}{\frac{{{(\sin x+\cos x)}^{2}}}{\sqrt{1+\sin 2x}}\text{ }}dx\]is    [AIEEE 2004]
  A)
                  3              done clear
  B)
                  1 done clear
  C)
                  2              done clear
  D)
                  0 done clear
  View Solution play_arrow

• question_answer101)
  \[\int_{0}^{\pi /8}{{{\cos }^{3}}4\theta d\theta }=\]                                        [Karnataka CET 2004]
  A)
                  \[\frac{2}{3}\]    done clear
  B)
                  \[\frac{1}{4}\] done clear
  C)
                  \[\frac{1}{3}\]    done clear
  D)
                  \[\frac{1}{6}\] done clear
  View Solution play_arrow

• question_answer102)
  \[\int_{3}^{8}{\frac{2-3x}{x\sqrt{(1+x)}}\text{ }}dx\]is equal to                                  [Pb. CET 2001]
  A)
                  \[2\log \,\left( 3/2{{e}^{3}} \right)\]        done clear
  B)
                  \[\log (3/{{e}^{3}})\] done clear
  C)
                  \[4\log (3/{{e}^{3}})\]    done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer103)
  The value of \[\int_{0}^{1}{{{x}^{2}}{{e}^{x}}dx}\]is equal to       [Pb. CET 2002]
  A)
                  \[e-2\]  done clear
  B)
                  \[e+2\] done clear
  C)
                  \[{{e}^{2}}-2\]   done clear
  D)
                  \[{{e}^{2}}\] done clear
  View Solution play_arrow

• question_answer104)
  Let \[{{I}_{1}}=\int_{1}^{2}{\frac{dx}{\sqrt{1+{{x}^{2}}}}}\]and\[{{I}_{2}}=\int_{1}^{2}{\frac{dx}{x}}\] then          [Pb. CET 2004]
  A)
                  \[{{I}_{1}}>{{I}_{2}}\]     done clear
  B)
                  \[{{I}_{2}}>{{I}_{1}}\] done clear
  C)
                  \[{{I}_{1}}={{I}_{2}}\]     done clear
  D)
                  \[{{I}_{1}}>2{{I}_{2}}\] done clear
  View Solution play_arrow

• question_answer105)
  The value of \[\int_{1/e}^{\tan x}{\frac{t\,dt}{1+{{t}^{2}}}}+\int_{1/e}^{\cot x}{\frac{dt}{t(1+{{t}^{2}})}}=\]        [IIT Screening]
  A)
                  \[-1\]     done clear
  B)
                  1 done clear
  C)
                  0              done clear
  D)
                  None of these done clear
  View Solution play_arrow

• question_answer106)
  \[\int\limits_{\pi /4}^{3\pi /4}{\frac{dx}{1+\cos x}}\] is equal to                                [IIT 1999]
  A)
                  2              done clear
  B)
                  \[-2\] done clear
  C)
                  \[\frac{1}{2}\]    done clear
  D)
                  \[-\frac{1}{2}\] done clear
  View Solution play_arrow

• question_answer107)
  The value of \[\int_{1}^{{{e}^{2}}}{\frac{dx}{x{{(1+\ln x)}^{2}}}}\] is                        [J & K 2005]
  A)
                  \[2/3\]  done clear
  B)
                  \[1/3\] done clear
  C)
                  \[3/2\]  done clear
  D)
                  \[\ln 2\] done clear
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• question_answer108)
  \[\int_{\pi /4}^{\pi /2}{\text{cose}{{\text{c}}^{2}}xdx=}\]                                            [Karnataka CET 2005]
  A)
                  \[-1\]     done clear
  B)
                  1 done clear
  C)
                  0              done clear
  D)
                  \[\frac{1}{2}\] done clear
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• question_answer109)
  If \[\int_{\log 2}^{x}{\frac{du}{{{({{e}^{u}}-1)}^{1/2}}}}=\frac{\pi }{6}\], then \[{{e}^{x}}=\]                        [Orissa JEE 2005]
  A)
  1 done clear
  B)
  2 done clear
  C)
  4              done clear
  D)
  -1 done clear
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• question_answer110)
  If \[g(1)=g(2)\], then \[\int_{1}^{2}{{{\left[ fg(x) \right]}^{-1}}}f'\{g(x)\}\ g'(x)\ dx\]is equal to                                                 [AMU 2005]
  A)
                  1              done clear
  B)
                  2 done clear
  C)
                  0              done clear
  D)
                  None of these done clear
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