Proving the Convolution Formula: Integral Equations

[icystrike]

Homework Statement

$$\int_{0}^{1} \int_{0}^{1} (xy) dx dy = [\int_{0}^{1} (x) dx] [\int_{0}^{1} (y) dy]$$

Its use to prove the convolution formula..

Homework Equations

The Attempt at a Solution

 

[Tangent87]

It's just standard separating multiple integrals, you could write the same thing with xy replaced by f(x)f(y).

 

[icystrike]

It's just standard separating multiple integrals, you could write the same thing with xy replaced by f(x)f(y).

But why is that so? Is it because the region of integration is rectangular?
Referring to Fubini Theorem

 

[Tangent87]

But why is that so? Is it because the region of integration is rectangular?
Referring to Fubini Theorem

No the region of integration does not have to be rectangular, it will work whenever the integral converges/exists, as you say Fubini's theorem: http://en.wikipedia.org/wiki/Fubini's_theorem