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If $-1 \leq x = y \leq 1$, and I am supposed to calculate double integral of $x^2 + y^2$, why won't this equal $0$? I know the answer is $0$ but when I calculate the integral using the limits $-1 \le x \le y$ and$-1 \le y <\le 1$, I do not get $0$.

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    This integral isn't equal zero. You have function that more than 0 in every point exept (0,0). It is positive.2012-01-23
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    Well, he *is* integrating over a region where $x=y$.2012-01-23
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    Do you mean to be integrating over $-1 \leq x = y \leq 1$ and not $-1 \leq x,y \leq 1$?2012-01-23
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    Yes, the former2012-01-23
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    Note the one-dimensional version of the problem: For real $x$'s let $f(x)= 2700000$, what is $\int_E f(x)dx$, where $E=\{0,3/5,1\}$?2012-01-24

4 Answers 4