Question

Check this integration:
Compute the volume under the graph of f(x,y)=x^2y on the region D in the first quadrent between the circles x^2+y^2=1 and x^2+y^2=4

Answer 1

I calculated the whole volume in the first quadrent first by using the double integral:\[\int\limits_{0}^{2}\int\limits_{0}^{4-x^2}x^2y\]

Answer 2

dydx

Answer 3

that gave me 64/30

Answer 4

That's not how you express the region between the 2 circles.

Answer 5

then how do you do it @blockcolder

Answer 6

That region is better expressed in polar coordinates.
\[D=\left \{ (r,\theta)|1\leq r\leq 2, 0\leq\theta\leq\pi/2\right \}\]
Use these bounds for D, and convert all x to r cos(theta), y to r sin(theta), and dy dx to r dr d(theta).

Answer 7

okay, i can understand that as maybe one way to do it, but so you are saying we cannot obtain the right answer doing it the way i did it

Answer 8

Technically you can, but yo'd have to divide the region into 2 parts, which will result in 2 double integrals.

Answer 9

can eloborate more on how to break it up into two parts

Answer 10

LOL forgive my circles. I'm using a laptop with no mouse right now.