I got a question in which I was asked to: Find the convolution of two time continuous functions- 3cos(2t) and a piece wise function in which the value of the function for t<0 is exp(t) and exp(-t) for t>0.
I know how to do the integral but I'm a bit confused on the limits. I usually integrate from 0 to t but they were not piece-wise functions. In this case the there is a part of the integral for t<0 but again we are integrating u. I have sawn some places where they have integrated the integral from positive to negative infinity. I'm confused on the limits and that's all. Please tell me what limits should be taken and if it is possible what exactly is u in basic terms.
Thank you for reading the question.
In general the integration is from $-\infty$ to $+\infty$. If you are convoluting two functions which vanish on $(-\infty,0)$ then the integral would be from from $0$ to $t$ because the integrand vanishes over the remaing part. In this case the integral is from $-\infty$ to $+\infty$.