Evaluate $\int_{0}^{\frac{\pi}{2}} \sin^{2} x \cos x\,dx$.

Explanation

1. 01

   An antiderivative is $F(x) = \frac{\sin^{3} x}{3}$.

2. 02

   By the fundamental theorem, the integral is $F(\frac{\pi}{2}) - F(0) = \frac{1}{3}$.