### Home > APCALC > Chapter 11 > Lesson 11.1.1 > Problem11-6

11-6.

Use the fact that $\cos(2θ)=2\cos^2(θ)-1$ to evaluate each of the following integrals.

1. $\int _ { 0 } ^ { 2 \pi } \operatorname { cos } ^ { 2 } ( \theta ) d \theta$

$=\frac{1}{2}\int_0^{2\pi}\Big(\cos(2\theta)+1\Big)d\theta$

1. $\int _ { 0 } ^ { 2 \pi } 4 \operatorname { sin } ^ { 2 } ( \theta ) d \theta$

$2\sin^2(\theta)=1-\cos(2\theta)$