JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

The value of the integral

\int\limits_{0}^\pi \frac{x \sin x}{1+\cos ^2 x} d x

View answer and explanation

Correct option: B

\frac{\pi^2}{4}

Option B (

\frac{\pi^2}{4}

) is correct because using the property

\int_0^a f(x) dx = \int_0^a f(a-x) dx

and then substituting

\cos x = t

, we can evaluate the definite integral to get

\frac{\pi^2}{4}

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