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JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

\lim\limits_{x \to \frac{\pi }{4}} \frac{{\int\limits_2^{{{\sec }^2}x} {f\left( t \right)dt} }}{{{x^2} - \frac{{{\pi ^2}}}{{16}}}}

equals

View answer and explanation

Correct option: A

\frac{8}{\pi} f(2)

Option A (

\frac{8}{\pi} f(2)

) is correct because it is the result of applying L'Hopital's rule to the limit and evaluating at

x = \frac{\pi}{4}

.

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[*]

denotes the greatest integer function, is The integral

\int\limits_{2}^4 \frac{\log x^2}{\log x^2+\log \left(36-12 x+x^2\right)} d x

is equal to: The definite integral

\int\limits_{{-2}}^0\left(x^3+3 x^2+3 x+3+(x+1) \cos (x+1)\right) d x

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I\,\,\left( {m + 1,\,\,n + 1} \right)