How Do You Integrate Convolution with Time-Shifted Unit Steps?

[Mr.Tibbs]

So here is my problem:
Find the output y(t) given the input x(t) and the input response h(t).

x(t) = e^-tu(t)

h(t) = u(t-2)-u(t-4)

Relevant equations:

y(t) = x(t)*h(t) = ∫e^-\tau u( \tau )(u(t-\tau-2)-u(t-\tau-4))d\tau

What I don't get:

How do I write h(t) in the integral? I think I'm just spacing this and it's going to be really easy but for the life of me I can't remember. So if I'm wrong in my relevant equations about how to set up h(t) would you mind correcting me?

Thanks

 

[aralbrec]

It looks right to me. When you want to write g(t-τ), you are replacing t in g(t) with (t-τ).

The integral would be easier to compute by hand if you switched around the convolution so that the pulse stays put.