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Math Help - Double integral problem

  1. #1
    Junior Member
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    Double integral problem

    Hi, I am having trouble with the following:

    Find the double integral of x+y, bounded by y=1 and y=x^2.

    I know the y integral will be between 0 and 1, but what will the x integral bounds be? because from what I can see by drawing the graph is that both the upper and lower bounds are y=x^2, but that doesn't make any sense.
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  2. #2
    Super Member
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    Re: Double integral problem

    I always have to draw a graph for these - or at least imagine one. You have a parabola and a horizontal line; the intersections are (-1,1) and (1,1). You get to choose whether to integrate y first or x first - I would have gone with y first, but it looks like you're doing x first. The right and left boundaries are the parabola, so solving for x gives x=-\sqrt{y} and x=\sqrt{y}. Then y goes from 0 to 1, as you said.

    If you integrate with respect to y first, then the top and bottom boundaries are the line and the parabola, so y goes from x^2 to 1. And then x goes from -1 to 1.

    - Hollywood
    Thanks from Paulo1913
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