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  4. If ∫ limits0π / 2 sin 4 x cos 8 x d x=(7 π/k) then find value of k.

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Q. If $\int\limits_{0}^{\pi / 2} \sin ^{4} x \cos ^{8} x d x=\frac{7 \pi}{k}$ then find value of $k$.

Integrals

Solution:

$I=\int\limits_{0}^{\pi / 2} \sin ^{4} x \cos ^{8} x d x$
$=\frac{(4-1)(4-3) \times(8-1)(8-3)(8-5)(8-7)}{12.10 .8 .6 .4 .2 .1} \frac{\pi}{2}$
$I=\frac{7 \pi}{2048}$