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Math Help - I'm really stuck! enclosed regions

  1. #1
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    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.
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  2. #2
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    Quote Originally Posted by eawolbert View Post
    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 = .....
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  3. #3
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    Thanks alot I totally forgot about getting the intersection points. I was trying to do it just up to 0. thanks a lot.
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