Question

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

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

Answer 1

Answer: (C)

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