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anonymous
 5 years ago
Can anyone help me integrate e^(x+y) for x,y>0
anonymous
 5 years ago
Can anyone help me integrate e^(x+y) for x,y>0

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{?}^{?}e^udu = e^(x+y) + C\]\[\int\limits_{?}^{?}\int\limits_{?}^{?}e^(xy)dxdy\], let u = xy, and take the partial derivative wrt x so du = 1\[\int\limits_{?}^{?}\int\limits_{?}^{?}e^ududy\] \[\int\limitse^(xy)dy\]. Now let u = xy and take the partial wrt y, du=1 so \[\int\limits_{?}^{?}e^udu=e^(x+y) + C\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you can do either dy or dx first, but it should still come out the same. Just remember that the u sub eliminates the second variable in du, because the partial derivs treat the other variable as a constant. Kind of like subbing u = 2x+3, du = 2dx, but in this here it's with x and y

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I think I get it. That subbing makes me dizzy but it'll catch on. Thanks.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0just remember, when subbing with two or more variables, your du's consist of partial derivatives.
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