JEE Main & Advanced Mathematics Definite Integration Question Bank

done Area Bounded by Region, Volume and Surface Area of Solids of Revolution Total Questions - 84

• question_answer1)
  Area bounded by the curve \[y=\log x\,,\] \[x-\]axis and the ordinates \[x=1,\,\,x=2\] is                                               [MP PET 2004]
  A)
             \[\log 4\]sq. unit                 done clear
  B)
             \[(\log 4+1)\]sq. unit done clear
  C)
             \[(\log 4-1)\]sq. unit          done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer2)
  Area bounded by the curve \[y=x{{e}^{{{x}^{2}}}},\] \[x-\]axis and the ordinates \[x=0,\,\,x=a\]
  A)
             \[\frac{{{e}^{{{a}^{2}}}}+1}{2}\]sq. unit                        done clear
  B)
             \[\frac{{{e}^{{{a}^{2}}}}-1}{2}\]sq. unit done clear
  C)
             \[{{e}^{{{a}^{2}}}}+1\]sq. unit                                           done clear
  D)
             \[{{e}^{{{a}^{2}}}}-1\]sq. unit done clear
  View Solution play_arrow

• question_answer3)
  Area bounded by the curve \[y=\sin x\] between \[x=0\] and \[x=2\pi \] is
  A)
             2 sq. unit                                 done clear
  B)
             4 sq. unit done clear
  C)
             8 sq. unit                                 done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer4)
  Area bounded by the parabola \[y=4{{x}^{2}},\] \[y-\]axis and the lines \[y=1,\,\,y=4\] is              [MNR 1990]
  A)
             3 sq. unit                                 done clear
  B)
             \[\frac{7}{5}\]sq. unit done clear
  C)
             \[\frac{7}{3}\]sq. unit        done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer5)
  Area bounded by the lines \[y=x,\,\,x=-1,\,\,x=2\] and \[x-\]axis is
  A)
             \[\frac{5}{2}\]sq. unit        done clear
  B)
             \[\frac{3}{2}\]sq. unit done clear
  C)
             \[\frac{1}{2}\]sq. unit        done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer6)
  If the ordinate \[x=a\] divides the area bounded by the curve \[y=\left( 1+\frac{8}{{{x}^{2}}} \right)\,,\] \[x-\]axis and the ordinates \[x=2,\] \[x=4\] into two equal parts, then \[a=\] [IIT 1983]
  A)
             8     done clear
  B)
             \[2\sqrt{2}\] done clear
  C)
             2     done clear
  D)
             \[\sqrt{2}\] done clear
  View Solution play_arrow

• question_answer7)
  Area between the curve \[y=\cos x\] and \[x-\]axis when \[0\le x\] is [MP PET 1997]
  A)
             2     done clear
  B)
             4 done clear
  C)
             0     done clear
  D)
             3 done clear
  View Solution play_arrow

• question_answer8)
  Area bounded by curve \[y={{x}^{3}},\] \[x-\]axis and ordinates \[x=1\] and \[x=4,\] is
  A)
             64 sq. unit                              done clear
  B)
             27 sq. unit done clear
  C)
             \[\frac{127}{4}\]sq. unit   done clear
  D)
             \[\frac{255}{4}\]sq. unit done clear
  View Solution play_arrow

• question_answer9)
  Area bounded by curve \[xy=c,\] \[x-\]axis between \[x=1\] and \[x=4,\] is
  A)
             \[c\log 3\]sq. unit               done clear
  B)
             \[2\log c\]sq. unit done clear
  C)
             \[2c\log 2\]sq. unit             done clear
  D)
             \[2c\log 5\]sq. unit done clear
  View Solution play_arrow

• question_answer10)
  Area bounded by curve \[y=k\sin x\]between \[x=\pi \] and \[x=2\pi ,\] is
  A)
             \[2k\] sq. unit                       done clear
  B)
             0 done clear
  C)
             \[\frac{{{k}^{2}}}{2}\] sq. unit                                           done clear
  D)
             \[k\] sq. unit done clear
  View Solution play_arrow

• question_answer11)
  Area bounded by \[y=x\sin x\] and \[x-\]axis between \[x=0\] and \[x=2\pi ,\] is                 [Roorkee 1981; RPET 1995]
  A)
             0     done clear
  B)
             \[2\pi \] sq. unit done clear
  C)
             \[\pi \] sq. unit                     done clear
  D)
             \[4\pi \] sq. unit done clear
  View Solution play_arrow

• question_answer12)
  Area under the curve \[y=\sin 2x+\cos 2x\] between \[x=0\] and \[x=\frac{\pi }{4},\] is                                 [AI CBSE 1979]
  A)
             2 sq. unit                                 done clear
  B)
             1 sq. unit done clear
  C)
             3 sq. unit                                 done clear
  D)
             4 sq. unit done clear
  View Solution play_arrow

• question_answer13)
  Area under the curve \[y=\sqrt{3x+4}\] between \[x=0\] and \[x=4,\] is                                               [AI CBSE 1979, 80]
  A)
             \[\frac{56}{9}\] sq. unit    done clear
  B)
             \[\frac{64}{9}\] sq. unit done clear
  C)
             8 sq. unit                                 done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer14)
  If area bounded by the curves \[{{y}^{2}}=4ax\] and \[y=mx\] is \[{{a}^{2}}/3,\],  then the value of \[m\] is
  A)
             2     done clear
  B)
             \[-2\] done clear
  C)
             \[\frac{1}{2}\]                       done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer15)
  Area bounded by parabola \[{{y}^{2}}=x\] and straight line \[2y=x\] is                                                    [MP PET 1996]
  A)
             \[\frac{4}{3}\]                       done clear
  B)
             1 done clear
  C)
             \[\frac{2}{3}\]                       done clear
  D)
             \[\frac{1}{3}\] done clear
  View Solution play_arrow

• question_answer16)
  Area bounded by lines \[y=2+x,\] \[y=2-x\] and \[x=2\] is                                                                       [MP PET 1996]
  A)
             3     done clear
  B)
             4 done clear
  C)
             8     done clear
  D)
             16 done clear
  View Solution play_arrow

• question_answer17)
  The ratio of the areas bounded by the curves \[y=\cos x\] and \[y=\cos 2x\] between \[x=0,\] \[x=\pi /3\] and \[x-\]axis, is                                                                       [MP PET 1997]
  A)
             \[\sqrt{2}:1\]                        done clear
  B)
             \[1:1\] done clear
  C)
             \[1:2\]                                      done clear
  D)
             \[2:1\] done clear
  View Solution play_arrow

• question_answer18)
  The area bounded by the curve \[y={{x}^{3}},\] \[x-\]axis and two ordinates \[x=1\] to \[x=2\] equal to                [MP PET 1999]
  A)
             \[\frac{15}{2}\] sq. unit    done clear
  B)
             \[\frac{15}{4}\] sq. unit done clear
  C)
             \[\frac{17}{2}\] sq. unit    done clear
  D)
             \[\frac{17}{4}\] sq. unit done clear
  View Solution play_arrow

• question_answer19)
  The area bounded by the \[x-\]axis and the curve \[y=\sin x\] and \[x=0,\] \[x=\pi \] is                                  [Kerala (Engg.) 2002]
  A)
             1     done clear
  B)
             2 done clear
  C)
             3     done clear
  D)
             4 done clear
  View Solution play_arrow

• question_answer20)
  The area bounded by the parabola \[{{y}^{2}}=4ax,\] its axis and two ordinates \[x=4,\] \[x=9\] is
  A)
             \[4{{a}^{2}}\]                        done clear
  B)
             \[4{{a}^{2}}.4\] done clear
  C)
             \[4{{a}^{2}}(9-4)\]              done clear
  D)
             \[\frac{152\sqrt{a}}{3}\] done clear
  View Solution play_arrow

• question_answer21)
  For \[0\le x\le \pi ,\] the area bounded by \[y=x\] and \[y=x+\sin x,\] is                [Roorkee Qualifying 1998]
  A)
             2     done clear
  B)
             4 done clear
  C)
             \[2\pi \]                                   done clear
  D)
             \[4\pi \] done clear
  View Solution play_arrow

• question_answer22)
  The area of the region bounded by the \[x-\]axis and the curves defined by \[y=\tan x,\,(-\pi /3\le x\le \pi /3)\] is [Kurukshetra CEE 1998]
  A)
             \[\log \sqrt{2}\]                   done clear
  B)
             \[-\log \sqrt{2}\] done clear
  C)
             \[2\log 2\]                              done clear
  D)
             0 done clear
  View Solution play_arrow

• question_answer23)
  If a curve \[y=a\sqrt{x}+bx\] passes through the point (1, 2) and the area bounded by the curve, line \[x=4\] and  x-axis is     8 sq. unit, then [MP PET 2002]
  A)
             \[a=3,\,b=-1\]                      done clear
  B)
             \[a=3,\,b=1\] done clear
  C)
             \[a=-3,\,b=1\]                      done clear
  D)
             \[a=-3,\,b=-1\] done clear
  View Solution play_arrow

• question_answer24)
  If the area above the x-axis, bounded by the curves \[y={{2}^{kx}}\] and \[x=0\] and \[x=2\] is \[\frac{3}{\ln 2},\] then the value of k is                                                                       [Orissa JEE 2003]
  A)
             \[\frac{1}{2}\]                       done clear
  B)
             1 done clear
  C)
             \[-1\]                                        done clear
  D)
             2 done clear
  View Solution play_arrow

• question_answer25)
  The area bounded by the x-axis, the curve \[y=f(x)\] and the lines \[x=1,\,x=b\] is equal to \[\sqrt{{{b}^{2}}+1}-\sqrt{2}\] for all b > 1, then \[f(x)\] is  \[\]                                   [MP PET 2000; AMU 2000]
  A)
             \[\sqrt{x-1}\]                        done clear
  B)
             \[\sqrt{x+1}\] done clear
  C)
             \[\sqrt{{{x}^{2}}+1}\]        done clear
  D)
             \[\frac{x}{\sqrt{1+{{x}^{2}}}}\] done clear
  View Solution play_arrow

• question_answer26)
  The area bounded by the curve \[y=f(x)\], x-axis and ordinates x = 1 and \[x=b\]is \[\frac{5}{24}\pi \], then \[f(x)\] is                    [RPET 2000]
  A)
             \[3(x-1)\cos (3x+4)+\sin (3x+4)\] done clear
  B)
             \[(b-1)\sin (3x+4)+3\cos (3x+4)\] done clear
  C)
             \[(b-1)\cos (3x+4)+3\sin (3x+4)\] done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer27)
  The area of the region (in the square unit) bounded by the curve \[{{x}^{2}}=4y,\] line \[x=2\] and x-axis is         [MP PET 2002]
  A)
             1     done clear
  B)
             \[\frac{2}{3}\] done clear
  C)
             \[\frac{4}{3}\]                       done clear
  D)
             \[\frac{8}{3}\] done clear
  View Solution play_arrow

• question_answer28)
  Area under the curve \[y={{x}^{2}}-4x\]within the x-axis and the line \[x=2\], is                                                [SCRA 1991]
  A)
             \[\frac{16}{3}sq.\,unit\]   done clear
  B)
             \[-\frac{16}{3}sq.\,unit\] done clear
  C)
             \[\frac{4}{7}sq.\,unit\]     done clear
  D)
             Cannot be calculated done clear
  View Solution play_arrow

• question_answer29)
  Area bounded by the curve \[xy-3x-2y-10=0,\]x-axis and the lines \[x=3,x=4\]is                                                [AI CBSE 1991]
  A)
             \[16\log 2-13\]                     done clear
  B)
             \[16\log 2-3\]                        done clear
  C)
             \[16\log 2+3\]                       done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer30)
  The area bounded by curve \[{{y}^{2}}=x,\] line \[y=4\] and y-axis is                          [Roorkee 1995; RPET 2003]
  A)
             \[\frac{16}{3}\]                    done clear
  B)
             \[\frac{64}{3}\] done clear
  C)
             \[7\sqrt{2}\]                          done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer31)
  The measurement of the area bounded by the co-ordinate axes and the curve \[y={{\log }_{e}}x\] is                     [MP PET 1998]
  A)
             1     done clear
  B)
             2 done clear
  C)
             3     done clear
  D)
             \[\infty \] done clear
  View Solution play_arrow

• question_answer32)
  Area bounded by the parabola \[{{y}^{2}}=2x\] and the ordinates \[x=1,x=4\] is
  A)
             \[\frac{4\sqrt{2}}{3}sq.\,unit\]                                         done clear
  B)
             \[\frac{28\sqrt{2}}{3}sq.\,unit\] done clear
  C)
             \[\frac{56}{3}\text{ }sq. unit\]                                          done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer33)
  The area bounded by the straight lines \[x=0,x=2\]and the curves \[y={{2}^{x}},y=2x-{{x}^{2}}\]is                                               [AMU 2001]
  A)
             \[\frac{4}{3}-\frac{1}{\log 2}\]                                           done clear
  B)
             \[\frac{3}{\log 2}+\frac{4}{3}\] done clear
  C)
             \[\frac{4}{\log 2}-1\]          done clear
  D)
             \[\frac{3}{\log 2}-\frac{4}{3}\] done clear
  View Solution play_arrow

• question_answer34)
  The area of smaller part between the circle \[{{x}^{2}}+{{y}^{2}}=4\]and the line \[x=1\] is           [RPET 1999]
  A)
             \[\frac{4\pi }{3}-\sqrt{3}\]      done clear
  B)
             \[\frac{8\pi }{3}-\sqrt{3}\]      done clear
  C)
             \[\frac{4\pi }{3}+\sqrt{3}\]     done clear
  D)
             \[\frac{5\pi }{3}+\sqrt{3}\] done clear
  View Solution play_arrow

• question_answer35)
  The area between the curve \[y={{\sin }^{2}}x,\] \[x-\]axis and the ordinates \[x=0\] and \[x=\frac{\pi }{2}\] is                    [RPET 1996]
  A)
             \[\frac{\pi }{2}\]                  done clear
  B)
             \[\frac{\pi }{4}\] done clear
  C)
             \[\frac{\pi }{8}\]                  done clear
  D)
             \[\pi \] done clear
  View Solution play_arrow

• question_answer36)
  The area bounded by the circle \[{{x}^{2}}+{{y}^{2}}=4,\] line \[x=\sqrt{3}y\] and \[x-\]axis lying in the first quadrant, is [RPET 1997; Kurukshetra CEE 1998]
  A)
             \[\frac{\pi }{2}\]                  done clear
  B)
             \[\frac{\pi }{4}\] done clear
  C)
             \[\frac{\pi }{3}\]                  done clear
  D)
             \[\pi \] done clear
  View Solution play_arrow

• question_answer37)
  The area of the triangle formed by the tangent to the hyperbola \[xy={{a}^{2}}\] and co-ordinate axes is              [RPET 2000]
  A)
             \[{{a}^{2}}\]                          done clear
  B)
             \[2{{a}^{2}}\] done clear
  C)
             \[3{{a}^{2}}\]                        done clear
  D)
             \[4{{a}^{2}}\] done clear
  View Solution play_arrow

• question_answer38)
  The area formed by triangular shaped region bounded by the curves \[y=\sin x,\,y=\cos x\] and \[x=0\] is           [MP PET 2000]
  A)
             \[x={{y}^{2}}\]                     done clear
  B)
             1 done clear
  C)
             \[\sqrt{2}\]                            done clear
  D)
             \[1+\sqrt{2}\] done clear
  View Solution play_arrow

• question_answer39)
  The part of straight line \[y=x+1\] between \[x=2\] and \[x=3\] is revolved about x-axis, then the curved surface of the solid thus generated is         [UPSEAT 2000]
  A)
             \[37\pi /3\]                            done clear
  B)
             \[7\pi \sqrt{2}\] done clear
  C)
             \[37\pi \]                                done clear
  D)
             \[y={{x}^{2}}\] done clear
  View Solution play_arrow

• question_answer40)
  The area bounded by the curve \[y=4x-{{x}^{2}}\] and the \[x-\]axis, is                                 [MP PET 1999, 2003]
  A)
             \[\frac{30}{7}\] sq. unit    done clear
  B)
             \[\frac{31}{7}\] sq. unit done clear
  C)
             \[\frac{32}{3}\] sq. unit    done clear
  D)
             \[\frac{34}{3}\] sq. unit done clear
  View Solution play_arrow

• question_answer41)
  Area of the region bounded by the curve \[y=\tan x,\] tangent drawn to the curve at \[x=\frac{\pi }{4}\] and the x-axis is       [DCE 2001]
  A)
             \[\frac{1}{4}\]                       done clear
  B)
             \[\frac{4}{3}\] done clear
  C)
             \[\log \sqrt{2}-\frac{1}{4}\]    done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer42)
  The area between the curve \[y=4+3x-{{x}^{2}}\] and  x-axis is                                                                       [RPET 2001]
  A)
             125/6                                        done clear
  B)
             125/3 done clear
  C)
             125/2                                        done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer43)
  The area bounded by the curve \[y=x,\] x-axis and ordinates \[x=-1\] to \[x=2\] is                                           [RPET 2001]
  A)
             0     done clear
  B)
             1/2 done clear
  C)
             3/2 done clear
  D)
             5/2 done clear
  View Solution play_arrow

• question_answer44)
  Area inside the parabola \[{{y}^{2}}=4ax,\]between the lines \[x=a\]and\[x=4a\]is equal to                    [Pb. CET 2002; Karnataka CET 2005]
  A)
             \[4{{a}^{2}}\]                        done clear
  B)
             \[8{{a}^{2}}\] done clear
  C)
             \[28\frac{{{a}^{2}}}{3}\]   done clear
  D)
             \[35\frac{{{a}^{2}}}{3}\] done clear
  View Solution play_arrow

• question_answer45)
  The area bounded by \[y=-{{x}^{2}}+2x+3\]and\[y=0\] is                                                                       [Orissa JEE 2004]
  A)
             \[32\]                                       done clear
  B)
             \[\frac{32}{3}\] done clear
  C)
             \[\frac{1}{32}\]                    done clear
  D)
             \[\frac{1}{3}\] done clear
  View Solution play_arrow

• question_answer46)
  The area enclosed between the curves \[y={{x}^{3}}\]and \[y=\sqrt{x}\] is, (in square units)                                         [Karnataka CET 2004]
  A)
             \[\frac{5}{3}\]                       done clear
  B)
             \[\frac{5}{4}\] done clear
  C)
             \[\frac{5}{12}\]                    done clear
  D)
             \[\frac{12}{5}\] done clear
  View Solution play_arrow

• question_answer47)
  The area between the parabola \[y={{x}^{2}}\] and the line \[y=x\] is                                                     [UPSEAT 2004]
  A)
             \[\frac{1}{6}\]sq. unit        done clear
  B)
             \[\frac{1}{3}\]sq. unit done clear
  C)
             \[\frac{1}{2}\]sq. unit        done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer48)
  Area bounded by the parabola \[{{y}^{2}}=4ax\] and its latus rectum is                                  [RPET 1997, 2000, 02]
  A)
             \[\frac{2}{3}{{a}^{2}}\]sq. unit                                          done clear
  B)
             \[\frac{4}{3}{{a}^{2}}\]sq. unit done clear
  C)
             \[\frac{8}{3}{{a}^{2}}\]sq. unit                                          done clear
  D)
             \[\frac{3}{8}{{a}^{2}}\]sq. unit done clear
  View Solution play_arrow

• question_answer49)
  Area enclosed by the parabola \[ay=3({{a}^{2}}-{{x}^{2}})\] and x-axis is
  A)
             \[4\,{{a}^{2}}\]sq. unit      done clear
  B)
             \[12\,{{a}^{2}}\]sq. unit done clear
  C)
             \[4\,{{a}^{3}}\]sq. unit      done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer50)
  Area of the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] is                 [Karnataka CET 1993]
  A)
             \[\pi \,ab\]sq. unit              done clear
  B)
             \[\frac{1}{2}\pi \,ab\]sq. unit done clear
  C)
             \[\frac{1}{4}\pi \,ab\]sq. unit done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer51)
  The area of the region bounded by \[y=\,\,|x-1|\] and \[y=1\] is                                                                       [IIT Screening 1994]
  A)
             2     done clear
  B)
             1 done clear
  C)
             \[\frac{1}{2}\]                       done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer52)
  The area between the curve \[{{y}^{2}}=4ax,\] x-axis and the ordinates \[x=0\] and \[x=a\] is                                    [RPET 1996]
  A)
             \[\frac{4}{3}{{a}^{2}}\]     done clear
  B)
             \[\frac{8}{3}{{a}^{2}}\] done clear
  C)
             \[\frac{2}{3}{{a}^{2}}\]     done clear
  D)
             \[\frac{5}{3}{{a}^{2}}\] done clear
  View Solution play_arrow

• question_answer53)
  The area of the curve \[x{{y}^{2}}={{a}^{2}}(a-x)\] bounded by y-axis is [RPET 1996]
  A)
             \[\pi {{a}^{2}}\]                    done clear
  B)
             \[2\pi {{a}^{2}}\] done clear
  C)
             \[3\pi {{a}^{2}}\]                 done clear
  D)
             \[4\pi {{a}^{2}}\] done clear
  View Solution play_arrow

• question_answer54)
  The area enclosed by the parabolas \[y={{x}^{2}}-1\] and \[y=1-{{x}^{2}}\] is                                      [AMU 1999]
  A)
             1/3 done clear
  B)
             2/3 done clear
  C)
             4/3 done clear
  D)
             8/3 done clear
  View Solution play_arrow

• question_answer55)
  The area of the smaller segment cut off from the circle \[{{x}^{2}}+{{y}^{2}}=9\] by \[x=1\] is                                     [RPET 2002]
  A)
             \[\frac{1}{2}(9{{\sec }^{-1}}3-\sqrt{8})\]                       done clear
  B)
             \[9{{\sec }^{-1}}(3)-\sqrt{8}\] done clear
  C)
             \[\sqrt{8}-9{{\sec }^{-1}}(3)\]                                            done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer56)
  The area of the region bounded by the curves \[y=|x-2|,\] \[x=1,\,\,x=3\]and the x-axis is                                          [AIEEE 2004]
  A)
             4     done clear
  B)
             2 done clear
  C)
             3     done clear
  D)
             1 done clear
  View Solution play_arrow

• question_answer57)
  The area enclosed between the parabolas \[{{y}^{2}}=4x\] and \[{{x}^{2}}=4y\] is              [Karnataka CET 1999, 2003]
  A)
             \[\frac{14}{3}\] sq. unit    done clear
  B)
             \[\frac{3}{4}\] sq. unit done clear
  C)
             \[\frac{3}{16}\] sq. unit    done clear
  D)
             \[\frac{16}{3}\] sq. unit done clear
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• question_answer58)
  The area bounded by the curves \[{{y}^{2}}=8x\] and \[y=x\] is
  A)
             \[\frac{128}{3}\] sq. unit  done clear
  B)
             \[\frac{32}{3}\] sq. unit done clear
  C)
             \[\frac{64}{3}\] sq. unit    done clear
  D)
             32 sq. unit done clear
  View Solution play_arrow

• question_answer59)
  The area bounded by the curves \[y={{\log }_{e}}x\] and \[y={{({{\log }_{e}}x)}^{2}}\] is                                               [RPET 2000]
  A)
             \[3-e\]                                     done clear
  B)
             \[e-3\] done clear
  C)
                      \[\frac{1}{2}(3-e)\]    done clear
  D)
                      \[\frac{1}{2}(e-3)\] done clear
  View Solution play_arrow

• question_answer60)
  The area between the parabola \[{{y}^{2}}=4ax\]and \[{{x}^{2}}=8ay\] is                                                               [RPET 1997]
  A)
             \[\frac{8}{3}{{a}^{2}}\]     done clear
  B)
             \[\frac{4}{3}{{a}^{2}}\] done clear
  C)
             \[\frac{32}{3}{{a}^{2}}\]   done clear
  D)
             \[\frac{16}{3}{{a}^{2}}\] done clear
  View Solution play_arrow

• question_answer61)
  The area of the region bounded by the curves \[y={{x}^{2}}\] and \[y=\,|x|\] is                                                [Roorkee 1999]
  A)
             1/6 done clear
  B)
             1/3 done clear
  C)
             5/6 done clear
  D)
             5/3 done clear
  View Solution play_arrow

• question_answer62)
  The area bounded by curves \[y=\cos x\] and \[y=\sin x\] and ordinates \[x=0\] and \[x=\frac{\pi }{4}\] is                               [Karnataka CET 2002]
  A)
             \[\sqrt{2}\]                            done clear
  B)
             \[\sqrt{2}+1\] done clear
  C)
             \[\sqrt{2}-1\]                        done clear
  D)
             \[\sqrt{2}(\sqrt{2}-1)\] done clear
  View Solution play_arrow

• question_answer63)
  The area in the first quadrant between \[{{x}^{2}}+{{y}^{2}}={{\pi }^{2}}\] and \[y=\sin x\] is                                      [MP PET 1997]
  A)
             \[\frac{({{\pi }^{3}}-8)}{4}\]   done clear
  B)
             \[\frac{{{\pi }^{3}}}{4}\] done clear
  C)
             \[\frac{({{\pi }^{3}}-16)}{4}\] done clear
  D)
             \[\frac{({{\pi }^{3}}-8)}{2}\] done clear
  View Solution play_arrow

• question_answer64)
  The area bounded by the curves \[{{y}^{2}}-x=0\] and \[y-{{x}^{2}}=0\] is                                            [MP PET 1997]
  A)
             \[\frac{7}{3}\]                       done clear
  B)
             \[\frac{1}{3}\] done clear
  C)
             \[\frac{5}{3}\]                       done clear
  D)
             1 done clear
  View Solution play_arrow

• question_answer65)
  The area of region \[\{\,(x,\,y):{{x}^{2}}+{{y}^{2}}\le 1\le x+y\}\] is                                                                                   [Kerala (Engg.) 2002]
  A)
             \[\frac{{{\pi }^{2}}}{5}\]   done clear
  B)
             \[\frac{{{\pi }^{2}}}{2}\] done clear
  C)
             \[\frac{{{\pi }^{2}}}{3}\]   done clear
  D)
             \[\frac{\pi }{4}-\frac{1}{2}\] done clear
  View Solution play_arrow

• question_answer66)
  The area of figure bounded by \[y={{e}^{x}},\,y={{e}^{-x}}\] and the straight line \[x=1\] is                                            [Karnataka CET 1999]
  A)
             \[e+\frac{1}{e}\]                 done clear
  B)
             \[e-3\] done clear
  C)
             \[e+\frac{1}{e}-2\]             done clear
  D)
             \[e+\frac{1}{e}+2\] done clear
  View Solution play_arrow

• question_answer67)
  The volume of the solid formed by rotating the area enclosed between the curve \[y={{x}^{2}}\] and the line \[y=1\] about \[y=1\] is (in cubic units [UPSEAT 2003]
  A)
             \[9\pi /5\]                              done clear
  B)
             \[4\pi /3\] done clear
  C)
             \[8\pi /3\]                              done clear
  D)
             \[7\pi /5\] done clear
  View Solution play_arrow

• question_answer68)
  The volume of the solid generated by revolving about the y-axis the figure bounded by the parabola \[y={{x}^{2}}\] and \[x={{y}^{2}}\] is                                                                        [UPSEAT 2002]
  A)
             \[\frac{21}{5}\pi \]              done clear
  B)
             \[\frac{24}{5}\pi \] done clear
  C)
             \[\frac{2}{15}\pi \]              done clear
  D)
             \[\frac{5}{24}\pi \] done clear
  View Solution play_arrow

• question_answer69)
  A frustum of sphere is made by cutting two parallel planes of any sphere. If radius of sphere is 5 cm and distance between the plane is 1 cm, then what will be the curved surface of frustum when the distance of first plane from the centre of sphere is 2 cm              [UPSEAT 1999]
  A)
             \[5\pi \,c{{m}^{2}}\]          done clear
  B)
             \[10\pi \,c{{m}^{2}}\] done clear
  C)
             \[15\pi \,c{{m}^{2}}\]        done clear
  D)
             \[40\pi \,c{{m}^{2}}\] done clear
  View Solution play_arrow

• question_answer70)
  The area enclosed by the parabola \[{{y}^{2}}=4ax\] and the straight line \[y=2ax,\] is                                    [MP PET 1993]
  A)
             \[\frac{{{a}^{2}}}{3}\] sq. unit                                           done clear
  B)
             \[\frac{1}{3{{a}^{2}}}\] sq. unit done clear
  C)
             \[\frac{1}{3a}\] sq. unit    done clear
  D)
             \[\frac{2}{3a}\] sq. unit done clear
  View Solution play_arrow

• question_answer71)
  The part of circle \[{{x}^{2}}+{{y}^{2}}=9\] in between \[y=0\] and \[y=2\] is revolved about y-axis. The volume of generating solid will be                        [UPSEAT 1999]
  A)
             \[\frac{46}{3}\pi \]              done clear
  B)
             \[12\pi \] done clear
  C)
             \[16\pi \]                                done clear
  D)
             \[28\pi \] done clear
  View Solution play_arrow

• question_answer72)
  Area bounded by the curve \[{{x}^{2}}=4y\] and the straight line \[x=4y-2\] is            [SCRA 1986; IIT 1981; Pb. CET 2003]
  A)
             \[\frac{8}{9}\] sq. unit       done clear
  B)
             \[\frac{9}{8}\] sq. unit done clear
  C)
             \[\frac{4}{3}\] sq. unit       done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer73)
  The area of the region bounded by the curve \[y=x|x|\],       x-axis and the ordinates \[x=1,\,\,x=-1\]is given by [Pb. CET 2004]
  A)
             Zero                                          done clear
  B)
   \[\frac{1}{3}\] done clear
  C)
             \[\frac{2}{3}\]                       done clear
  D)
             1 done clear
  View Solution play_arrow

• question_answer74)
  Area included between the two curves \[{{y}^{2}}=4ax\] and \[{{x}^{2}}=4ay,\] is        [SCRA 1986; Roorkee 1984; RPET 1999; Kerala (Engg.) 2002, 05]
  A)
             \[\frac{32}{3}\,{{a}^{2}}\] sq. unit                                   done clear
  B)
             \[\frac{16}{3}\] sq. unit done clear
  C)
             \[\frac{32}{3}\] sq. unit    done clear
  D)
             \[\frac{16}{3}\,{{a}^{2}}\] sq. unit done clear
  View Solution play_arrow

• question_answer75)
  If the area bounded by \[y=a{{x}^{2}}\]and \[x=a{{y}^{2}}\], \[a>0\], is 1, then \[a=\]                    [IIT Screening 2004]
  A)
             1     done clear
  B)
             \[\frac{1}{\sqrt{3}}\] done clear
  C)
             \[\frac{1}{3}\]                       done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer76)
  The area bounded by the curves \[y=\sqrt{x},\] \[2y+3=x\] and \[x-\]axis in the 1st quadrant is                    [IIT Screening 2003]
  A)
             9     done clear
  B)
             \[\frac{27}{4}\] done clear
  C)
             36   done clear
  D)
             18 done clear
  View Solution play_arrow

• question_answer77)
  The area enclosed between the curve \[y={{\log }_{e}}(x+e)\]and the co-ordinate axes is                                            [AIEEE 2005]
  A)
             3     done clear
  B)
             4 done clear
  C)
             1     done clear
  D)
             2 done clear
  View Solution play_arrow

• question_answer78)
  The parabolas \[{{y}^{2}}=4x\] and \[{{x}^{2}}=4y\] divide the square region bounded by the lines \[x=4\], \[y=4\]and the coordinate axes. If \[{{S}_{1}},{{S}_{2}},{{S}_{3}}\] are respectively the areas of these parts numbered from top to bottom, then \[{{S}_{1}}:{{S}_{2}}:{{S}_{3}}\] is                                                            [AIEEE 2005]
  A)
             \[2:1:2\]                                  done clear
  B)
             \[1:1:1\]                                  done clear
  C)
             \[1:2:1\]                                  done clear
  D)
             \[1:2:3\] done clear
  View Solution play_arrow

• question_answer79)
  If A is the area of the region bounded by the curve \[y=\sqrt{3x+4}\], x axis and the line \[x=-1\] and \[x=4\]and B is that area bounded by curve \[{{y}^{2}}=3x+4\], x- axis and the lines \[x=-1\]and \[x=4\] then \[A:B\] is equal to [J& K 2005]
  A)
             \[1:1\]                                      done clear
  B)
             \[2:1\] done clear
  C)
             \[1:2\]                                      done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer80)
  The area of the region bounded by the curve \[9{{x}^{2}}+4{{y}^{2}}-36=0\] is                                   [Karnataka CET 2005]
  A)
             \[9\pi \]                                   done clear
  B)
             \[4\pi \] done clear
  C)
             \[36\pi \]                                done clear
  D)
             \[6\pi \]                                   done clear
  View Solution play_arrow

• question_answer81)
  The area bounded by the curve \[y={{(x+1)}^{2}},\,y={{(x-1)}^{2}}\] and the line \[y=\frac{1}{4}\] is                                           [IIT Screening 2005]
  A)
             1/6 done clear
  B)
             2/3 done clear
  C)
             1/4 done clear
  D)
             1/3 done clear
  View Solution play_arrow

• question_answer82)
  Let \[f(x)\] be a non-negative continous function such that the area bounded by the curve \[y=f(x)\], x-axis and the ordinates \[x=\frac{\pi }{4}\], \[x=\beta >\frac{\pi }{4}\] is \[\left( \beta \sin \beta +\frac{\pi }{4}\cos \beta +\sqrt{2}\beta  \right)\]. Then \[f\ \left( \frac{\pi }{2} \right)\] is                                               [AIEEE 2005]
  A)
             \[\left( 1-\frac{\pi }{4}-\sqrt{2} \right)\]                       done clear
  B)
             \[\left( 1-\frac{\pi }{4}+\sqrt{2} \right)\] done clear
  C)
             \[\left( \frac{\pi }{4}+\sqrt{2}-1 \right)\]                      done clear
  D)
             \[\left( \frac{\pi }{4}-\sqrt{2}+1 \right)\] done clear
  View Solution play_arrow

• question_answer83)
  Area bounded by curves \[y={{x}^{2}}\] and \[y=2-{{x}^{2}}\] is                                                                                         [Orissa JEE 2005]
  A)
             8/3 done clear
  B)
             3/8 done clear
  C)
             3/2 done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer84)
  Let y be the function which passes through (1, 2) having slope \[(2x+1)\]. The area bounded between the curve and   x-axis is   [DCE 2005]
  A)
             6 sq. unit                                 done clear
  B)
             5/6 sq. unit done clear
  C)
             1/6 sq. unit                            done clear
  D)
             None of these done clear
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