Solve ∫ (from 0 to 180) of |cosθ|d0

$$\int _ { 0 } ^ { 180 } | \cos \theta | d 0$$

Evaluate

$$180d_{0}|\cos(\theta )|$$

Solution Steps

Evaluate the indefinite integral first.

$$\int |\cos(\theta )|d_{0}\mathrm{d}x$$

Find the integral of |\cos(\theta )|d_{0} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$|\cos(\theta )|d_{0}x$$

The definite integral is the antiderivative of the expression evaluated at the upper limit of integration minus the antiderivative evaluated at the lower limit of integration.

$$180|\cos(\theta )|d_{0}+0|\cos(\theta )|d_{0}$$

Simplify.

$$180|\cos(\theta )|d_{0}$$

Differentiate w.r.t. θ

$$-180d_{0}\sin(\theta )sign(\cos(\theta ))$$