Systems and signals – integration with dirac’s function and step function


I'm taking the introductory course to systems and signals and the mathematics of integration using the step function and Dirac's function

integral 1


problem 2

For the first integral, I just don't know how to deal with u(t-4), the step function.

The other two questions i don't even know how to start. Thanks, any help would be appreciated

Best Answer

u(t-4) means that the integral is equal to zero till you reach 4, so compute the integral from 4 to infinity. the last question, it's about convolution of h(t) and x(t). for x(t), t<0 always x(t)=0, t=0 x(t) = 1 and t>0 x(t)= -1. draw x(t), you have h(t). convolve them.