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anonymous

  • 5 years ago

Can anyone help me integrate e^-(x+y) for x,y>0

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  1. anonymous
    • 5 years ago
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    \[\int\limits_{?}^{?}e^udu = e^-(x+y) + C\]\[\int\limits_{?}^{?}\int\limits_{?}^{?}e^(-x-y)dxdy\], 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
    • 5 years ago
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    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
    • 5 years ago
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    I think I get it. That subbing makes me dizzy but it'll catch on. Thanks.

  4. anonymous
    • 5 years ago
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    just remember, when subbing with two or more variables, your du's consist of partial derivatives.

  5. anonymous
    • 5 years ago
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    Thx

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