Setting the limits on an integral for a joint pdf

• Apr 6th 2009, 11:32 PM
veol
Setting the limits on an integral for a joint pdf
Hi everyone!

I'm trying to solve a double integral to find the joint pdf of a function, but I'm not sure as to how to set the limits.

$\displaystyle f(x, y) = c(x^2 - y^2)e^{-x}$

with $\displaystyle 0 \leq x, -x \leq y \leq x$

I have to solve for the constant, c, so I thought that solving the double integral in the range of x and y and making that equal to 1 would solve for c, but I'm having trouble integrating. I suspect its my bounds for the integral.

I'm not quite sure.... for my integration of the x values, I set the limits from 0 to infinity, and for the y values, the limits i set were from -x to x. Is that right?

Many thanks!
• Apr 6th 2009, 11:56 PM
matheagle
It seems to be $\displaystyle 1=\int_0^{\infty}\int_{-x}^x f(x,y)dydx$.
• Apr 6th 2009, 11:58 PM
veol
Yeah, that's what I thought it would be as well. I just remember setting the limits to double integrals as being tricky for some odd reason... I felt unsure of myself.

Thanks for the heads up, matheagle!
• Apr 7th 2009, 12:11 AM
matheagle
You should always draw the region. You draw the lines y=x and y=-x.
It is the region between those two in the first and fourth quadrants since x is nonnegative.