1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How to solve this double integral?

  1. Mar 10, 2012 #1
    1. The problem statement, all variables and given/known data


    $$\left[\int\limits_0^{Inf} {\int\limits_0^{Inf} {e^{ - aX - bY} \cdot F(X + Y + c)} }\cdot X^d \cdot Y^e \cdot dX \cdot dY\right]$$
    2. Relevant equations
    a,b,c are constants; d & e are non negative integers; X and Y are variables.
    F is a one to one function. Please simplify. The answer is in single Integrals. Leave the Function F as it is.



    3. The attempt at a solution
    put X+Y=V, Y=U
     
    Last edited: Mar 10, 2012
  2. jcsd
  3. Mar 10, 2012 #2
     
    Last edited: Mar 10, 2012
  4. Mar 10, 2012 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Try two dollar signs, $ $ without the space, at both ends:
    $$\left[\int\limits_0^{Inf} {\int\limits_0^{Inf} {e^{ - aX - bY} \cdot F(X + Y + c)} }\cdot X^d \cdot Y^e \cdot dX \cdot dY\right]$$
    I also changed "\[" and "\]" to "\left[" and "\right]",.

    Without knowing the function F, I don't see any way to simplify that.
     
  5. Mar 10, 2012 #4
    F is a one to one function. Please simplify in such a way that the answer is left out with only a single Integral. Please simplify as much as possible. Leave the Function F as it is.
     
  6. Mar 10, 2012 #5

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    hi vineel49! :smile:
    well, the obvious way is to make X + Y + c one of two new variables, and then integrate wrt the other :wink:
     
  7. Mar 10, 2012 #6
    It is not that simple, I am trying since morning on this one.
     
  8. Mar 10, 2012 #7

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    what did you get when you tried it? :smile:
     
  9. Mar 10, 2012 #8
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: How to solve this double integral?
Loading...