# Thread: I'm really stuck! enclosed regions

1. ## I'm really stuck! enclosed regions

Hi, this is the problem: Sketch the region enclosed by x+y2=12 and x+y=0. Decide whether to integrate with respect to x or y. Then find the area of the region.

I set the equations equal to x because it seemed easier. then i graphed them to see the area enclosed. i tried to take the integral from -3.4641 to zero after substracting both equations but can't get the right answer.
any help will be appreciated.

2. Originally Posted by eawolbert
Hi, this is the problem: Sketch the region enclosed by x+y2=12 and x+y=0. Decide whether to integrate with respect to x or y. Then find the area of the region.

I set the equations equal to x because it seemed easier. then i graphed them to see the area enclosed. i tried to take the integral from -3.4641 to zero after substracting both equations but can't get the right answer.
any help will be appreciated.
The points of intersection are (-4, 4) and (3, -3):

Substitute x = -y into x + y^2 = 12:

-y + y^2 = 12 => y^2 - y - 12 = 0 => (y - 4)(y + 3) = 0 => y = 4, -3.

I'd suggest it's easiest to integrate wrt y:

Area = int[-3, 4] (12 - y^2) - (-y) dy = .....

3. Thanks alot I totally forgot about getting the intersection points. I was trying to do it just up to 0. thanks a lot.