Question

The value of the integral ${\int }_{-\frac{\pi }{4}}^{\frac{\pi }{4}}{\sin }^{3}xdx$ is

• A. $3/2$
• B. $0$
• C. $3/8$
• D. $8/3$

Answer 1

The correct option is B $0$

We've,

${\int }_{-\frac{\pi }{4}}^{\frac{\pi }{4}}{\sin }^{3}xdx$ $=0$. [ Since $\underset{-a}{\overset{a}{\int }}f\left(x\right)dx=0$ for $f\left(x\right)$ being odd].

For the given integral $f\left(x\right)={\sin }^{3}x$.

Now, $f(-x)=-{\sin }^{3}x=-f\left(x\right)$$\forall x\in R$.

So $f\left(x\right)$ is odd function.