The value of the integral $\mathop \smallint \limits_0^\pi \,\,\frac{{x\,dx}}{{1 + \cos \,\,\alpha \,\,\sin \,\,x}},\;\,0 < \alpha < \pi $, is

$\frac{{\pi \alpha }}{{1 + \sin \,\,\alpha }}$

$\frac{{\pi \alpha }}{{\cos \,\,\alpha }}$

$\frac{{\pi \alpha }}{{1 + \cos \,\,\alpha }}$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

The value of the integral

\int \limits_0^\pi \,\,\frac{{x\,dx}}{{1 + \cos \,\,\alpha \,\,\sin \,\,x}},\;\,0 < \alpha < \pi

, is

View answer and explanation

Correct option: A

\frac{{\pi \alpha }}{{\sin \,\alpha }}

Option A (

\frac{{\pi \alpha }}{{\sin \alpha }}

) is correct because the integral is solved using properties of definite integrals and trigonometric substitutions.

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