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Math Help - Double Integral Problem.

  1. #1
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    Double Integral Problem.

    I'm trying to calculate the following problem, however, when I take the integral of G with respect to y, my limits tend towards infinity. I can only think of using polar co-ordinates to solve this, but I'm not sure how it would apply in a case where one of the limits is 3-7y...

    Let G be the region described by the inequalities 0 ≤ x ≤ 3 − 7y
    and 0 ≤ y. Present a sketch of the region G and calculate the
    double integral of the function f (x, y) = 2x + y^2 over G.
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  2. #2
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    This integral should work:

    \int _0 ^3 \int _0 ^{3-7y} (2x + y^2) dx \cdot dy
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  3. #3
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    Thanks, how did you get the three? I'm assuming you substituted y=0 in the limit 3-7y
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  4. #4
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    Quote Originally Posted by Penguin91 View Post
    Thanks, how did you get the three? I'm assuming you substituted y=0 in the limit 3-7y
    Sorry, I made a mistake. The correct integral should be

    \int _0 ^{3/7} \int _0 ^{3-7y} (2x + y^2) dx \cdot dy

    Solve x = 3-7y for y and you get the correct result.
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