Question

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

Answer 1

Answer: 2048.00

$I=\underset{0}{\overset{\pi /2}{\int }}{\sin }^{4}x{\cos }^{8}xdx$
$=\frac{(4-1)(4-3)\times (8-1)(8-3)(8-5)(8-7)}{\mathrm{12.10.8.6.4.2.1}}\frac{\pi }{2}$
$I=\frac{7\pi }{2048}$