Question

I=∫∫xydxdy. x^2+y^2≤7

Answer 1

\[ \int_{-\sqrt 7 }^{\sqrt 7} \int_{-\sqrt{7 - x^2}}^{\sqrt{7 - x^2}} xy \; dy dx\]

Answer 2

In polar coordinates
\[ \int_0^\sqrt7 \int_0^{2 \pi} r^3\sin \theta \cos \theta d\theta dr\]

Answer 3

yes

Answer 4

let her work it out she needs some practice setting up integrals

Answer 5

you scared me. i tried to do it on my on and i jumped straight to polar. why r^3? probably a stupid question but i need to understand it not just find out the answer

Answer 6

because rdrdtheta = polar
and x = rcostheta
y=rsintheta