Chapter 11.4, Problem 24E

To determine

(a)

To draw the spiral curve of $r\left(\theta \right)=\theta$.

To determine

(b)

To find out the area enclosed by the curve $r\left(\theta \right)=\theta$ for $6\pi \le \theta \le 8\pi$.

To determine

(c)

To show that the increase in area enclosed by the graph of $r\left(\theta \right)=\theta$ as $\theta$ goes from $2n\pi$ to $\text{ 2}\left(n+1\right)\pi$ is $\text{ 8n}{\pi }^3$.