What is the Convolution of a Unit Step Function and an Exponential Function?

[Quincy]

Homework Statement

h(t) = u(t) (the unit step function)

x (t) = e^-t

The Attempt at a Solution

There is only one interval where the two functions overlap, and that's from 0 to t.

The integral from 0 to t of e^-\tau d\tau = -e^-t

Doesn't look right to me... what am I doing wrong?

EDIT: This is discrete convolution, by the way.

 

[vela]

e⁰=1