Define
Spiral of Archimedes: 
for 
.
Sketch this graph in polar coordinates and compute the area of the radial set.
The sketch is as follows:
Then, we compute the area,
![\[ a(R) = \frac{1}{2} \int_0^{2 \pi} \theta^2 \, d \theta = \frac{1}{2} \frac{(2 \pi)^3}{3} = \frac{4 \pi^3}{3}. \]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-22af961c016bd7a3f39e71cc279133d0_l3.png "Rendered by QuickLaTeX.com")
Define
Spiral of Archimedes: for .
Sketch this graph in polar coordinates and compute the area of the radial set.
The sketch is as follows:
Then, we compute the area,