# Convolution in Continious time

Dear all,

Please find attached image, I am not able to understand why is the underlined term is to be included. Shouldn't it be simply the exponential term?

• Paste the link to the image in plain text and someone will edit it in for you – jonsca Dec 22 '13 at 9:24
• OK, It must be visible now. – aditya Dec 22 '13 at 9:44

The $u(t-2)$ term needs to be included because the upper limit of the definite integral is $t-2$, not $\infty$:
• The upper limit is $\infty$ because of the definition of convolution: you are summing up the effect of impulses at all times $t' \in (-\infty, \infty)$ at the current time $t$. It just so happens that in this particular case, your system only turns on for t>2, i.e. your impulse response is only non-zero for that time interval, so you can equivalently write the convolution integral with the upper limit $t-2$. – Sina Dec 22 '13 at 16:58