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Math Help - Double intergral

  1. #1
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    Question Double intergral

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    I usually know how to do double integrals, but i have no idea how to deal with this one. plz help me solve/understand this.
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  2. #2
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    Quote Originally Posted by DMDil View Post
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    I usually know how to do double integrals, but i have no idea how to deal with this one. plz help me solve/understand this.
    The integrand is seperable in the variables: x e^x y e^y. So it becomes the product of two seperate integrals, each of which can be done using integration by parts.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by DMDil View Post
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    I usually know how to do double integrals, but i have no idea how to deal with this one. plz help me solve/understand this.
    integrate with respect to y first and then with respect to x, plugging in the limits as you go. note, when integrating with respect to y, treat x as a constant, and vice versa.

    you need integration by parts here. to start off, let u = xy and dv = e^{x + y}~dy (remember, x is a constant!)

    Quote Originally Posted by mr fantastic View Post
    The integrand is seperable in the variables: x e^x y e^y. So it becomes the product of two seperate integrals, each of which can be done using integration by parts.
    hehe, even nicer
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  4. #4
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    Quote Originally Posted by DMDil View Post
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    I usually know how to do double integrals, but i have no idea how to deal with this one. plz help me solve/understand this.
    Since you're on a rectangle and the expontential spilts up then

    \int_4^7 x e^x dx \int_5^7 y e^y dy then parts on each part.
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