anonymous
  • anonymous
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?
OCW Scholar - Multivariable Calculus
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
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?
phi
  • phi
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!

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