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Math Help - double integral, triangular region

  1. #1
    Junior Member
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    double integral, triangular region

    I need to solve the double integral for y^3, where the region (D) is a triangle with vertices (0,2) (1,1) (3,2).

    So first I drew out these points, made the triangle, and then solved the equation of each of the three triangle lines.
    So for (0,2) to (1,1), i got y=-x
    for (3,2) to (0,2), i got y=2
    for (3,2) to (1,1), i got y= x/2 +1/2

    so then i decided to integrate with respect to x first. i solved the two line equations for x, and found that -y < x < 2y-1
    and 1 < y < 2. so those would be my bounds for x and y.

    then i integrated y^3 dxdy. which gives me first: xy^3. plug in the bounds, and i got 2y^4-y^3+y^4.

    then integrated that for y. plugged in the bounds and solved and got 297/20. i'm told the answer is 147/20. i have tried doing it with y first, and using two different sets of bounds for y but i'm not getting it. i don't know what other way there is to try...

    what am i doing wrong here?
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  2. #2
    MHF Contributor
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    So for (0,2) to (1,1), i got y=-x
    the equation of this line is y=-x + 2


    if you carry that change forwards will you get the right answer?
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