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Math Help - Double integral - me & book ans disagree

  1. #1
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    Double integral - me & book ans disagree

    Hello, I've been studying double integrals over non-rectangular regions and have been having a bit of trouble but think I've cracked it. However, the book answer and me disagree on the following question; Mathematica agrees with me but I thought maybe I was using the wrong region. The question is:

    Find the volume of the solid which is below the plane z=2x+3 and above the xy-plane and bounded by y^2=x, x=0, x=2.

    The region, R, in the xy-plane I'm evaluating over is R=\{(x,y) | 0 \le y \le x^{1/2}, 0 \le x \le 2\} and the final answer I get is  \frac{36}{5} \sqrt{2}. Whereas the book gets \frac{14}{5} \sqrt{2}.

    Could somebody verify if I'm using the right region and what the actual answer is?

    Thanks,

    triptyline
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  2. #2
    Eater of Worlds
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    Here's the correct set up:

    \int_{0}^{\sqrt{2}}\int_{0}^{y^{2}}(2x+3)dxdy
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  3. #3
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    Yep, your quite right - I've evaluated over the wrong region.
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