Question

The value of the integral $\int \sin x{\cos }^{4}xdx$ where $x\in [-1,1]$ is

• A. 1
• B. 1\2
• C. 0
• D. 4

Answer 1

Answer: (C)

0

$f\left(x\right)=\sin x{\cos }^{4}x,$

$f(-x)=\sin (-x){\cos }^4(-x)=-f\left(x\right)$

Since $f\left(x\right)$ is an odd function, ${\int }_{-1}^1\sin x{\cos }^{4}xdx=0$