Mathematics

$\displaystyle\int_{0}^{\pi}\frac{dx}{1+a^{\cos x}}$ equals

$\displaystyle\frac{\pi }{2}$

SOLUTION
$\displaystyle I=\int _{ 0 }^{ \pi } \frac { dx }{ 1+a^{ \cos x } } =\int _{ 0 }^{ \pi } \frac { dx }{ 1+a^{ \cos \left( \pi -x \right) } } =\int _{ 0 }^{ \pi } \frac { dx }{ 1+a^{ -\cos x } } =\int _{ 0 }^{ \pi } \left( 1-\frac { 1 }{ 1+a^{ \cos x } } \right) dx$
$\Rightarrow I=\pi -I$
$\Rightarrow I=\dfrac { \pi }{ 2 }$

Ans: B

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

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