Question

${\int }_{-1}^1{x}^{17}{\cos }^{4}xdx$ is equals to

• A. $-2$
• B. $2$
• C. $0$
• D. $1$

Answer 1

The correct option is C $0$

$I={\int }_{-1}1x^{17}{\cos }^{4}x.dx$

$f\left(x\right)=x^{17}{\cos }^{4}x$

$f(-x)=(-x{)}^{17}{\cos }^4(-x)=-x^{17}{\cos }^{4}x=f(-x)$

$\therefore$ f is an odd function.

$\therefore {\int }_{-a}^{a}f\left(x\right)dx=0\therefore I={\int }_{-1}^{1}f\left(x\right)dx=0$