Mathematics

# The value of $\int _{ 0 }^{ \pi /2 }{ \cfrac { \sin { x } -\cos { x } }{ 1+\sin { x } \cos { x } } } dx$ is ____

$0$

##### SOLUTION
Let
$I=\displaystyle \int_{0}^{\pi/2}{\dfrac{\sin x-\cos x dx}{1+\sin x\cos x}}-----(1)$
using $\displaystyle \int_{a}^{b}{f(x)dx}=\displaystyle \int_{a}^{b}{f(a+b-x)dx}$
$I=\displaystyle \int_{0}^{\pi/2}{\dfrac{\cos x-\sin x dx}{1+\sin x\cos x}}-----(2)$
$(1)+(2)$
$2I=\displaystyle \int_{0}^{\pi/2}{\dfrac{\sin x-\cos x+\cos x-\sin x}{1+\sin x\cos x}}dx$
$2I=0\Rightarrow I=0$

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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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