When I tried the first convolution, I yielded the correct result over the desired regions of overlap, but for the second, I did not.

**Method 1**

\(y(t) = g(t)\ast v(t) = \int_{-\infty}^{\infty}g(\tau)v(\tau-t)d\tau\)

**Method 2**

\(y(t) = v(t)\ast g(t) = \int_{-\infty}^{\infty}v(\tau)g(\tau-t)d\tau\) (did not receive correct result)

__Region 1__

**t <= 0**;

\(y(t_{1}) = 0\)

__Region 2__

t >= 0 and (t-2) <= 0

**0 <= t <= 2**;

\(y(t_{2}) = \int_{0}^{t}(exp{-\tau})(2exp{2(\tau -t)})d\tau\)

\(= 2exp{-2t}\int_{0}^{t}exp{\tau}d\tau\)

\(=2exp{-2t}(exp{t} - 1)\)

**The answer for this region should be:**

\(y(t_{2}) = 2exp{-t}(1 - exp{-t})\)

I got the correct result when I flipped and shifted v(t) as in Method 1, which is weird because they should be commutative.

Can anyone see where I went wrong?

Thanks,

JP