Question

Evaluate the integral

${\int }_0^{\pi /2}{\sin }^{4}xdx$

• A. $\frac{\pi }{12}$
• B. $\frac{3\pi }{7}$
• C. $\frac{3\pi }{16}$
• D. $0$

Answer 1

Answer: (C)

$\frac{3\pi }{16}$

${\int }_0^{\frac{\pi }{2}}si{n}^{4}xdx$

${\int }_0^{\frac{\pi }{2}}si{n}^{n}xdx=\frac{(n-1)}{n}\frac{(n-3)}{(n-2)}\frac{(n-5)}{(n-4)}....I_0$

${\int }_0^{\frac{\pi }{2}}si{n}^{4}xdx=\frac{3}{4}\times \frac{1}{2}\times I_0$

$=\frac{3}{4}\times \frac{1}{2}\times \frac{\pi }{2}$

$=\frac{3\pi }{16}$