Question

Show that:

${\int }_{-1}^1{x}^{17}{\cos }^{4}xdx=0$.

• A. 2
• B. 1
• C. 0
• D. 3

Answer 1

The correct option is C 0

Now,

$\underset{-1}{\overset{1}{\int }}{x}^{17}{\cos }^{4}xdx=0$. [ Using the property of definite integration of odd function]

Since the function $f\left(x\right)=x^{17}{\cos }^{4}x$ is an odd function as $f(-x)=-f\left(x\right)$ for all $x$.