JEE Main & Advanced Mathematics Definite Integration Question Bank

done Numerical Value Type Questions - Definite Integration Total Questions - 15

• question_answer1)
  If \[f\left( x \right)=\frac{{{e}^{x}}}{1+{{e}^{x}}},{{I}_{1}}=\int\limits_{f\left( -a \right)}^{f\left( a \right)}{xg\left( x\left( 1-x \right) \right)\,dx}\] and \[{{I}_{2}}=\int\limits_{f\left( -a \right)}^{f\left( a \right)}{g\,\,\left( x\left( 1-x \right) \right)\,\,dx,}\] then find the value of \[\frac{{{I}_{2}}}{{{I}_{1}}}.\]
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• question_answer2)
  Find the value of \[\int\limits_{-2}^{2}{\left| \left[ x \right] \right|}\,\,dx\](where [.] denotes greatest integer function)
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• question_answer3)
  Evaluate: \[\int\limits_{-1}^{1}{\log \left( x+\sqrt{{{x}^{2}}+1} \right)dx}\]
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• question_answer4)
  Evaluate: \[\int\limits_{\pi }^{10\pi }{\left| \sin x \right|dx}\]
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• question_answer5)
  If \[\int\limits_{0}^{\pi /8}{{{\cos }^{3}}4\,\theta }\,\,d\theta \] is equal to \[\frac{2}{\lambda }\] then find \[\lambda \].
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• question_answer6)
  Evaluate: \[\int_{-\pi /2}^{\pi /2}{\frac{\cos x}{1+{{e}^{x}}}dx}\]
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• question_answer7)
  If \[{{I}_{n}}=\int\limits_{0}^{\pi /4}{{{\tan }^{n}}xdx}\,\,\text{and}\,\,{{I}_{8}}+{{I}_{6}}=\frac{1}{\lambda }\] then find \[\lambda \].
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• question_answer8)
  If \[\int\limits_{0}^{1}{\frac{{{\tan }^{-1}}x}{1+{{x}^{2}}}dx=\frac{{{\pi }^{2}}}{k}}\]then find value of k.
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• question_answer9)
  Find the value of integral\[\int\limits_{-1}^{1}{\left| 1-x \right|\,\,dx}\].
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• question_answer10)
  If \[\int\limits_{0}^{a}{\frac{{{x}^{7}}dx}{\sqrt{{{a}^{2}}-{{x}^{2}}}}=\frac{k}{\lambda }{{a}^{7}}}\]then find value of\[\lambda -k\].
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• question_answer11)
  If \[\int\limits_{0}^{\pi /2}{{{\sin }^{4}}x{{\cos }^{8}}x\,\,dx}=\frac{7\pi }{k}\] then find value of k.
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• question_answer12)
  Evaluate: \[\int\limits_{0}^{200\pi }{\sqrt{\frac{1-\cos \,\,2x}{2}}dx}\]
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• question_answer13)
  If \[\int\limits_{0}^{\pi /2}{\frac{\sqrt{\sin x}}{\sqrt{\operatorname{sinx}}+\sqrt{\cos \,\,x}}dx=\frac{\pi }{\lambda }}\]then find the value of\[\lambda \].
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• question_answer14)
  Find the value of\[\int\limits_{0}^{2014}{\frac{{{2}^{x}}}{{{2}^{x}}+{{2}^{2014-x}}}dx}\].
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• question_answer15)
  If \[\int_{0}^{1}{{{x}^{6}}\sqrt{1-{{x}^{2}}}dx}=\frac{\lambda \pi }{k}\]then find\[\lambda +k\].
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