Question

The value of ${\int }_{-8}^8({\sin }^{93}x+x^{295})dx$

• A. $1$
• B. $-1$
• C. $0$
• D. $\frac{8}{3}$

Answer 1

The correct option is C $0$

Let $\text{f}\left(x\right)={\sin }^{93}x+x^{295}$

Now $\text{f}(-x)=-{\sin }^{93}x-x^{295}$, since odd powers

$\Rightarrow \text{f}\left(x\right)$ is an odd function

Hence ${\int }_{-8}^8\text{f}\left(x\right)dx=0$, Property