Question

can someone tell me how they would set up the bounds for a double integral above a circle (x-2)^2+y^2=4. Not in polar coords.

Answer 1

so you want bounds in r and theta or x and y?

Answer 2

x and y

Answer 3

I know r and theta is easier but, I want to wrap my head better around setting up the bounds in x and y

Answer 4

normally you dont need to find bounds in x and y from r and theta. since knowing bounds in r and theta is just a method to find double integration that have bounds in x and y.
Anyway, in this case, the circle has center (2,0) radius 2, so theta runs from 0 to pi/4 and r from 0 to 4
wait... I think im confused too lol

Answer 5

I'd say 0 <= x <=4
and y<= sqrt(4-(x-2)^2)
but I dont know what <=y

Answer 6

It would be easier to integrate taking the x and y terms and changing them over to polar, but I want to keep it all in xand y and I'm confused on how I make sure that I stay in the circle, and not set up something wierd and inaccurate. I thought about 2 *\[\int\limits_{0}^{\sqrt{4-(x-2)^2}} dx\] for dx, but I don't think I can go -2 to 2 for dy. I know I could do y= -root for the circle in stead of o for the lower bound in dx, but I'd rather just multiply the sum I listed by two. I just don't know about the dy limits, though.

Answer 7

yeah that's also what confused me. that 0 is not quite right. It cut the circle in half. I prefer something that would intergrate the full circle so that we dont need to time 2.
May need to ask someone about this. But I don't think they will ever ask to find x and y bounds from r, theta
oh no, I think that's actually right. I was thinking ∫dy but if you have ∫dx there, that will bound the whole circle, then the bound for y is -2 to 2 is fine, because ∫∫dxdy = ∫∫dydx

Answer 8

so the dy bound is good then, man, I was confusing the mess out of myself.

Answer 9

yeah it's good. When you change ∫∫dxdy to ∫∫dydx, you need to change the bounds for x and y, but the meaning of the total bound remain the same.

Answer 10

right on, thanks for your help

Answer 11

well actually that's u helped me lol. totally forget about changing order