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Thread: How to solve int[-2,-1] int[0,y+2] e^((x+y)/(x-y)) dx dy w/o Jacobian method?

  1. #1

    How to solve int[-2,-1] int[0,y+2] e^((x+y)/(x-y)) dx dy w/o Jacobian method?

    How to solve this double integral without Jacobian method?

    . . . . .[tex]\displaystyle \large{ \int_{-2}^{-1}\, \int_0^{y+2}\, e^{\left(\frac{x+y}{x-y}\right)}\, dx\, dy }[/tex]
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    Last edited by stapel; 11-30-2017 at 05:07 PM. Reason: Typing out the text in the graphic; creating useful subject line.

  2. #2
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    Quote Originally Posted by salar14666 View Post
    How to solve this double integral without Jacobian method?

    . . . . .[tex]\displaystyle \large{ \int_{-2}^{-1}\, \int_0^{y+2}\, e^{\left(\frac{x+y}{x-y}\right)}\, dx\, dy }[/tex]
    1) Why? If it can be expressed simply, why do you care how it is done?
    2) "Jacobian Method"? Do you mean an astute variable substitution?
    3) Occasionally, some advantage can be had by a simple reversal of the order of integration.
    4) You could add the Cauchy Principle Value Exponential Integral to your canon of thought.
    5) There is a reason why we invented Numerical Methods. Is it Real Valued?
    Last edited by stapel; 11-30-2017 at 05:08 PM. Reason: Copying typed-out graphical content into reply.
    "Unique Answers Don't Care How You Find Them." - Many may have said it, but I hear it most from me.

  3. #3
    Quote Originally Posted by tkhunny View Post
    1) Why? If it can be expressed simply, why do you care how it is done?
    2) "Jacobian Method"? Do you mean an astute variable substitution?
    3) Occasionally, some advantage can be had by a simple reversal of the order of integration.
    4) You could add the Cauchy Principle Value Exponential Integral to your canon of thought.
    5) There is a reason why we invented Numerical Methods. Is it Real Valued?
    Could you please solve it in simplest form??

  4. #4
    Elite Member stapel's Avatar
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    Cool

    Quote Originally Posted by salar14666 View Post
    Could you please solve it in simplest form??
    Please reply with answers to the helper's questions. When you reply, please include a clear listing of your thoughts and efforts so far, so we can see where you're getting stuck. Thank you!

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