Question

The value of $\underset{0}{\overset{\pi }{\int }}{\sin }^{50}x{\cos }^{49}xdx$ is

• A. $0$
• B. $\pi /4$
• C. $\pi /2$
• D. $1$

Answer 1

Answer: (A)

Let $I=\underset{0}{\overset{\pi }{\int }}{\sin }^{50}x{\cos }^{49}xdx$
$=\underset{0}{\overset{\pi }{\int }}{\sin }^{50}(\pi -x){\cos }^{49}(\pi -x)dx$
$=-\underset{0}{\overset{\pi }{\int }}{\sin }^{50}x{\cos }^{49}xdx$
$\Rightarrow I=-I\Rightarrow I=0$