# Homework Help: How to solve this double integral?

1. Mar 10, 2012

### vineel49

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. Mar 10, 2012

### vineel49

Last edited: Mar 10, 2012
3. Mar 10, 2012

### HallsofIvy

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.

4. Mar 10, 2012

### vineel49

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.

5. Mar 10, 2012

### tiny-tim

hi vineel49!
well, the obvious way is to make X + Y + c one of two new variables, and then integrate wrt the other

6. Mar 10, 2012

### vineel49

It is not that simple, I am trying since morning on this one.

7. Mar 10, 2012

### tiny-tim

what did you get when you tried it?

8. Mar 10, 2012