Math Help - Double Integral

1. Double Integral

Let
f be continuous on [0; 1] and let R be the triangular region with vertices (0; 0); (1; 0) and (0; 1). Show that

$\int\int_{R}f(X+Y)=\int_{0}^{1}uf(u)\, du$

Hi All,

I got stuck with the above question. Basically I got LHS:
$\int\int_{R}f(X+Y)=\int_{0}^{1}\int_{0}^{1-x}f(x+y)\, dydx$

How do I continue from here?

2. Hi QF203 classmate. Use the change of variable method taught in Lesson 9. Haha. Use u=x+y, and v=y.

3. Originally Posted by metallicsatan
Hi QF203 classmate. Use the change of variable method taught in Lesson 9. Haha. Use u=x+y, and v=y.
You will also need to compute the Jacobian so that $\displaystyle dy\,dx$ is transformed to $\displaystyle |J|\,du\,dv$ or $\displaystyle |J|\,dv\,du$ (whichever is easier).

4. Thanks for the help. I had a similar problem too.