Question

Change the Cartesian integral int[0 to 9]int[0 to y]x dx dy into an equivalent polar integral.

Answer 1

\[\int\limits_{0}^{9}\int\limits_{0}^{y}x \ dx dy\] I know the first part is
\[\int\limits_{0}^{9/\sin }\] but I don't know the second part

Answer 2

Yeah, this is just sort of a silly integral to transform.

Answer 3

any thoughts? I have the first part:
\[\int\limits_{?}^{?}\int\limits_{0}^{9/\sin (\theta)}r ^{2}\cos \theta \ dr d \theta \]

Answer 4

@mahmit2012

Answer 5

y=x isn't it?

Answer 6

I mean for the original integral

Answer 7

yes 0<x<y

Answer 8

I would say you integrate from 45% until 90%

so \( \large \frac{\pi}{4}< \theta< \frac{\pi}{2} \)