# How do you find the area of the region bounded by the spiral r=7theta for 0<=theta<=pi?

$A = \frac{1}{2} {\int}_{\Delta \theta} {r}^{2} d \theta$
$= \frac{1}{2} {\int}_{0}^{\pi} {\left(7 \theta\right)}^{2} d \theta$
$= \frac{49}{2} {\left[{\theta}^{3} / 3\right]}_{0}^{\pi}$
$= \frac{49}{6} {\pi}^{3}$