How do convolutions work with a heaviside function?

for example, if f(t) = t^2 and g(t)=u(t-1), how do i find f*g?

By definition, you have



Take and . Then



The Heaviside step function is defined as



and adjusting its argument by 1, you have



which means the integral reduces to



This integral doesn't converge, but hopefully it's a simple enough demonstration of how you might go about computing such an integral.