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

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

Hi All,

I got stuck with the above question. Basically I got LHS:

$\displaystyle \int\int_{R}f(X+Y)=\int_{0}^{1}\int_{0}^{1-x}f(x+y)\, dydx$

How do I continue from here?