Double integral

**Andreamet** · February 5th 2009, 04:21 PM

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

$<br /> \int_0^1 \int_0^1 max\{x,y\} * e^{max\{x^2,y^2\}} dx dy <br />$

**Opalg** · February 6th 2009, 03:20 AM

Originally Posted by Andreamet

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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