Module 4: Trigonometry Review: Integrals

Some integrals can be simplified by using a trigonometric identity. This is not a general method, and only works for certain very specific integrals. Since these integrals do come up with some frequency it is worth knowing the double angle trick and its variations.
For example, check out this integral:

$LaTeX: \begin{align*} \int \sin^2 (x)\; dx &= \int \left( \frac{1-\cos(2x)}{2}\right) \; dx\; \; \;\;\;\mbox{(Remembering one of the double angle formulas)}\\ &= \int \frac{1}{2} -\frac{\cos(2x)}{2}\; dx\\ &=\frac{x}{2}-\frac{\sin(2x)}{4}+C \end{align*}$ $\begin{align*} \int \sin^2 (x)\; dx &= \int \left( \frac{1-\cos(2x)}{2}\right) \; dx\; \; \;\;\;\mbox{(Remembering one of the double angle formulas)}\\ &= \int \frac{1}{2} -\frac{\cos(2x)}{2}\; dx\\ &=\frac{x}{2}-\frac{\sin(2x)}{4}+C \end{align*}$