Question

Solve ${\int }_0^{\frac{\pi }{2}}{\sin }^{2}x\cos xdx$

• A. $\frac{2}{3}$
• B. $\frac{5}{3}$
• C. $\frac{1}{3}$
• D. $-\frac{1}{3}$

Answer 1

The correct option is C $\frac{1}{3}$

Consider the given integral.

$I={\int }_0^{\frac{\pi }{2}}{\sin }^{2}x\cos xdx$

Let $t=\sin x$

$dt=\cos xdx$

Therefore,

$I={\int }_0^1{t}^{2}dt$

$I={\left[\frac{t^3}{3}\right]}_0^1$

$I=[\frac{1}{3}-0]$

$I=\frac{1}{3}$

Hence, this is the answer.