Question

Evaluate: $\int_{0}^{\pi} sin^{3}x \,dx$

Answer 1

$\frac{4}{3}$

Answer 2

Write $\sin^3x$ as $\sin x(1-\cos^2 x)$. Substitute $u=\cos x$ and convert limits. Evaluate the resulting integral $\int_{-1}^{1}(1-u^2)du$ to get $\frac{4}{3}$.