How can I use direct integration to solve for the convolution of two signals?

[Vanush]

Hey guys, I'm having trouble doing ct convolution

i'm trying to convolve two signals together ie, the input x(t) and the impulse response h(t). basically, knowing the impulse response of an LTI system, you can find out the response y(t) to any arbitrary input x(t) using the convolution integral.

in my problem

x(t) = t * ( u(t) - 2*( u(t - 1) + u(t - 2)),
h(t) = u(-t) - u(-t + 1)

So i had a look at examples of calculating the integral using the graphical method, and i get a triangle signal as y(t), convolving the signals above. however, the question wants me to do it using direct integration. I have no idea how to do this! Anyone have any ideas?

 

[HallsofIvy]

What is u(t)?

 

[Vanush]

Unit step function

 

[Defennder]

He wasn't asking you what that notation meant, but how you should think of interpreting what it means when integrating it.

 

[Vanush]

THat's the thing, when I put it into the integral I have to work out a bunch of inequalities that really makes my head spin. This question is so much harder than the example :(