Question

Identify the correct representation of integral of odd function on a symmetric interval.
${\int }_{-a}^{a}f\left(x\right)dx$

• A. $-1$
• B. $1$
• C. $0$
• D. None of these

Answer 1

The correct option is C $0$

Given : ${\int }_{-9}^{9}f\left(x\right)dx$

Since, $f\left(x\right)$ is odd function

$f\left(x\right)=-f(-x)$

Then,

${\int }_{-9}^{0}f\left(x\right)dx=-{\int }_0^{9}f\left(x\right)dx{\int }_{-9}^{9}f\left(x\right)dx={\int }_0^{9}f\left(x\right)dx+{\int }_{-9}^{0}f\left(x\right)dx=-{\int }_{-9}^{0}f\left(x\right)dx+{\int }_{-9}^{0}f\left(x\right)dx=0$

Hence the correct answer is $0$.