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Math Help - integrating e^(x+y)

  1. #1
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    Question integrating e^(x+y)

    i am working on some problems involving triple integrals and a lot of them have e^(x+y) but i just don't get how to integrate this with respect to x or y.

    can somebody please explain me how this works?

    Thanks
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  2. #2
    MHF Contributor Calculus26's Avatar
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    Candy

    If you integrate e^(x+1) I'm sure you'd say e^(x+1) and you'd be right

    When intergrating e^(x+y) wrt x treat y as a constant

    When integratin e^(x+y) wrt y treat as x as a constant

    In either case you get e ^(x+y)
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  3. #3
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by Calculus26 View Post
    Candy

    If you integrate e^(x+1) I'm sure you'd say e^(x+1) and you'd be right

    When intergrating e^(x+y) wrt x treat y as a constant

    When integratin e^(x+y) wrt y treat as x as a constant

    In either case you get e ^(x+y)
    You need to bring the 1/constant out too because of integration by parts (or whatever the opposite of the chain rule is)

    If x is constant and with respect to y:

    \int e^{x+y}dy = e^{x+y} + C

    If y is constant and with respect to x:

    \int e^{x+y}dx = e^{x+y} + C
    Last edited by e^(i*pi); April 20th 2009 at 05:41 AM. Reason: Integration error, see post below
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  4. #4
    MHF Contributor Calculus26's Avatar
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    e^ipi

    your formula is for integrating e^(xy) not e^(x+y)
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  5. #5
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    Now, what if i want to integrate ∫∫∫ ze^(x+y) dV to find the mass of the rectangular box determined by 0≤x≤1, 0≤y≤1 and 0≤z≤5.

    i tried to solve the integral in the following order..
    ∫from 0 to 1 ∫from 0 to 1 ∫from 0 to 5 (ze^(x+y))dzdydx
    i use the method Calculus 26 described and i got 58.38 but it's wrong!
    can you tell mewhat i did wrong, is my set up right?

    Thank you
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  6. #6
    MHF Contributor Calculus26's Avatar
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    See attachment
    Attached Files Attached Files
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  7. #7
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    now i get it, thanks
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  8. #8
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    \iint e^{x+y}dxdy=\iint e^x e^y dxdy = \left(\int e^x dx\right)\left(\int e^y dy\right)
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