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  4. ∫ limits0π / 2 √ sin θ cos 3 θ d θ is equal to

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Q. $\int\limits_{0}^{\pi / 2} \sqrt{\sin \theta} \cos ^{3} \theta d \theta$ is equal to

KCETKCET 2022Integrals

Solution:

Put $\sin \theta= t$
$\int\limits_{0}^{1} t^{1 / 2}\left(1-t^{2}\right) d t=\frac{8}{21}$