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  4. ∫ limits0π / 2 ( cos x sin x/1+ sin x) d x is equal to

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Q. $\int\limits_{0}^{\pi / 2} \frac{\cos x \sin x}{1+\sin x} d x$ is equal to

KCETKCET 2022Integrals

Solution:

$\sin x=t$
$\int\limits_{0}^{\frac{\pi}{2}} \frac{\cos x \sin x}{1+\sin x} d x $
$\Rightarrow \int\limits_{0}^{1} \frac{t}{1+t} d t=1-\log 2$