Question

In Session 65 (Green's Theorem), there seems to be a mistake in the example (Using Green's Theorem). The double integral is calculated as 16*pi/3; shouldn't it be 8pi?

Answer 1

In the fourth equation in the example PDF, it says, \[\int\limits_{0}^{2\pi}\int\limits_{0}^{2}r^{2}rdrd \theta = \int\limits_{0}^{2\pi}\frac{ 8 }{ }\], but shouldn't it be \[\int\limits_{0}^{2\pi}4d \theta\] because the antiderivative of r^3 is r^4/4?

Answer 2

Apparently they overlooked the factor of r from dA = r dr dtheta
and integrated r^2 to get r^3/3 and then 8/3
oops!