Question

Iterated integrals

Answer 1

\[\int\limits_{0}^{2}\int\limits_{0}^{\pi}rsin^2\theta d\theta dr\]

Answer 2

what this means s that
the integration re

Answer 3

region is \[0\le r\le2,\qquad 0\le\theta\le\pi\]

Answer 4

then we check, if theta and r are independent of eachother in the given problem. they are and hence can be integrated as individuals

Answer 5

\[I=\left(\int_{r=0}^2r\,dr\right)\times\left(\int_{\theta=0}^\pi\sin^2\theta\;d\theta\right)\]

Answer 6

the first paranthesis is straightforward
for the theta integral, convert sin^2 theta using: \(\cos2\theta=1-2\sin^2\theta\)

Answer 7

Oh okay thanks! I was struggling especially with the sin^2