Solution assignment 05 Integration by substitution

Solve:

$\displaystyle\int_{0}^{\pi}\cos(2x)dx$

The primitive of the integrand is:

$\sin(2x)\cdot\displaystyle\frac{1}{2}$

This result is correct which can be verified by differentiation. The chain rule has to be applied. Thus:

$\displaystyle\int_{0}^{\pi}\cos(2x)dx=\displaystyle\frac{1}{2}[\sin(2x)]_{0}^{\pi}=\displaystyle\frac{1}{2}[\sin(2\pi)-\sin(0)]=0$