Question

$\underset{-8}{\overset{8}{\int }}({\sin }^{93}x+x^{295})dx=$

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

Answer 1

Answer: (C)

$\underset{-8}{\overset{8}{\int }}({\sin }^{93}x+x^{295})dx$
$=\underset{-8}{\overset{8}{\int }}{\sin }^{93}xdx+\underset{-8}{\overset{8}{\int }}{x}^{295}dx=0$
$[\therefore$ Using $\underset{-a}{\overset{a}{\int }}f(x)dx=0,$ if $f(x)$ is an odd function $]$
$\because x^{295}$ and ${\sin }^{93}x$ are odd functions