Polar Form Question 4

calculator allowed The graph above shows the polar curve $r=2\theta + \cos{\theta}$ for $0\leq \theta \leq \pi$ . What is the area of the region bounded by the curve and the $x$ -axis?

3.069

9.870

17.456

34.912

Approach

\frac{1}{2}\int \limits_a^b (r(\theta))^2   d\theta

\frac{1}{2}\int \limits_0^\pi (2\theta+\cos{\theta})^2   d\theta

\approx \boxed{17.456}