Question

The value of integral ${\int }_{-3/2}^{3/2}{\sin }^{3}x{\cos }^{2}xdx$ is

• A. $0$
• B. $1/2$
• C. $1$
• D. None of these

Answer 1

Answer: (A)

$0$

Let $I={\int }_{-3/2}^{3/2}{\sin }^{3}x{\cos }^{2}xdx$

$f\left(x\right)={\sin }^{3}x{\cos }^{2}x$

$f(-x)={\sin }^3(-x){\cos }^2(-x)=-{\sin }^{3}x{\cos }^{2}x=-f\left(x\right)$

$\therefore$ $f\left(x\right)$ is an odd function

$\therefore$ $I=0$