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

1. anonymous

$\int\limits_{?}^{?}e^udu = e^-(x+y) + C$$\int\limits_{?}^{?}\int\limits_{?}^{?}e^(-x-y)dxdy$, let u = -x-y, and take the partial derivative wrt x so du = -1$\int\limits_{?}^{?}-\int\limits_{?}^{?}e^ududy$ $\int\limits-e^(-x-y)dy$. Now let u = -x-y and take the partial wrt y, du=-1 so $\int\limits_{?}^{?}e^udu=e^-(x+y) + C$

2. anonymous

you 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

3. anonymous

I think I get it. That subbing makes me dizzy but it'll catch on. Thanks.

4. anonymous

just remember, when subbing with two or more variables, your du's consist of partial derivatives.

5. anonymous

Thx