Mathematics

# The value of $\displaystyle\int\limits_{0}^{\dfrac{\pi}{2}}\dfrac{2^{\sin x}}{2^{\sin x}+2^{\cos x}}dx$ is

$\dfrac{\pi}{4}$

##### SOLUTION
Let $I=$$\displaystyle\int\limits_{0}^{\dfrac{\pi}{2}}\dfrac{2^{\sin x}}{2^{\sin x}+2^{\cos x}}dx......(1). or, I=$$\displaystyle\int\limits_{0}^{\dfrac{\pi}{2}}\dfrac{2^{\cos x}}{2^{\cos x}+2^{\sin x}}dx$ [ Using property of definite integral]......(2).
$2I=$$\displaystyle\int\limits_{0}^{\dfrac{\pi}{2}}dx=\dfrac{\pi}{2}$
or, $I=\dfrac{\pi}{4}$.

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 111

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