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Math Help - Double integral

  1. #1
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    Double integral

    I have no idea how to solve the double integral for the function. Could I get some help please?

    <br />
\int_0^1 \int_0^1 max\{x,y\} * e^{max\{x^2,y^2\}} dx dy <br />
    Last edited by Andreamet; February 5th 2009 at 05:20 PM.
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  2. #2
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    Quote Originally Posted by Andreamet View Post
    I have no idea how to solve the double integral for the function. Could I get some help please?

    <br />
\int_0^1 \int_0^1 \max\{x,y\} * e^{\max\{x^2,y^2\}} dx dy <br />
    Here's a non-rigorous (but essentially correct) way to tackle this. For 0 ≤ t ≤ 1, the set \{(x,y):\max\{x,y\}=t\} is L-shaped, consisting of two line segments each of length t. Thus it has "infinitesimal area" 2tdt, and therefore \int_0^1 \!\!\int_0^1\!\! \max\{x,y\} * e^{\max\{x^2,y^2\}}\, dx\, dy = \int_0^1\!\!te^{t^2}2t\,dt. You can integrate this by parts, but the answer will have to involve the error function. Numerically, I make it approx. 1.9715.
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