Question

$$ int - \frac { cos 2 \theta } { 2 } d \theta $$

Explanation:

Step1: Integrate the function

The integral of \(\cos(ax)\) with respect to \(x\) is \(\frac{\sin(ax)}{a}+C\). Here \(a = 2\) and we have \(-\frac{1}{2}\cos(2\theta)\).

$$
LATEXBLOCK0
$$

Let \(u = 2\theta\), then \(du=2d\theta\) or \(d\theta=\frac{1}{2}du\).

$$
LATEXBLOCK1
$$

Substituting back \(u = 2\theta\)

$$=-\frac{\sin(2\theta)}{4}+C$$

Answer:

\(-\frac{\sin(2\theta)}{4}+C\)