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#### Petrus

##### Well-known member

- Feb 21, 2013

- 739

I got as homework to solve this problem and get recomend to solve it with polar but I have not really work with polar but we have had lecture about it and I have done some research. This is the problem and what I understand

\(\displaystyle \int\int_Dx^3y^2\ln(x^2+y^2)\), \(\displaystyle 4\leq x^2+y^2\leq 25\) and \(\displaystyle x,y\geq 0\)

if we want to change it to polar form lets write \(\displaystyle x=r\cos\theta\) and \(\displaystyle y=r\sin\theta\)

so we got:

\(\displaystyle \int_{\theta_1}^{\theta_2}\int_{r_1}^{r_2}r^3\cos^3\theta*r^2\sin^2\theta \ln(r^2\cos^2\theta+r^2\sin^2\theta) \ drd\theta\)

and we got our identity that \(\displaystyle x^2+y^2=r^2\) that means we got our r limit as \(\displaystyle 2\leq r \leq 5\) if I am thinking correct we can't use our negative limit cause it says \(\displaystyle x,y\geq 0\) I am stuck with how to get my \(\displaystyle \theta\) limit well so far I can think we know that \(\displaystyle 4 \leq r^2cos^2\theta + r^2sin^2\theta \leq 25\) here is what I strugle with. is solve limit for \(\displaystyle \theta\)

Regards,