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

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Answer 1 · 2018-07-14T00:25:03

$A = 1/2 int_(Delta theta) r^2 d theta$

$= 1/2 int_0^pi (7theta)^2 d theta$

$= 49/2 [theta^3/3]_0^pi$

$= 49/6 pi^3$

The graphing tool can't seem to handle this, and there is no draw tool here, so I found this image online:

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How do you find the area of the region bounded by the spiral r=7thetar=7theta for 0<=theta<=pi0<=theta<=pi?