Hello, I've once again run into a small hurdle in my quest to learn maths on my own, with no one to talk to about it except for you fine folk! So If you would, please lend a hand again, I really do appreciate it!

The question is:

A linear, time invariant system has the impulse response

find the system response to the input

Now, I know the answer is

My answer is

Now I can see how to get to that answer. I'm taking the limits of the integral as follows:

But I guess it should be

Can anyone help to explain why you need the upper limit to be three? Surely when

is less than 3, you don't want

to go beyond 3? But then in my example, you don't want

to go beyond 3 when

is more than 3... So that doesn't make sense really either...

(I do grasp the logic behind convolution, can visualise what is happening, and can implement it in some basic signal processing. It's just parts of the mathematical proof that get to me!)