The value of the integral $\mathop \smallint \limits_0^\pi \,\,\frac{1}{{{a^2} - \,\,2a\,\,\cos \,\,x\,\, + \,\,1}}\,\,dx\,\,(a < 1)$ is

$\frac{\pi }{{{a^2}\,\, - \,\,1}}$

$\frac{{2\;\pi }}{{{a^2}\,\, - \,\,1}}$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

The value of the integral

\int \limits_0^\pi \,\,\frac{1}{{{a^2} - \,\,2a\,\,\cos \,\,x\,\, + \,\,1}}\,\,dx\,\,(a < 1)

View answer and explanation

Correct option: A

\frac{\pi }{{1\,\, - \,\,{a^2}}}

Option A (

\frac{\pi }{{1\,\, - \,\,{a^2}}}

) is correct because after applying trigonometric identities and substitution, the integral evaluates to the given expression.

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