A signal f(t)= 2.5 t and a second signal g(t)= 4 t^2 are convolved. Using the fundamental definition of convolution, f(t)⊛g(t)= lim(0→t) ∫f(τ)g(t−τ)dτ, find the value of the convolution at t = 3 seconds.
Hint: Write the integral as lim(0→t) ∫g(τ)f(t−τ)dτ where the two signals are as specified above. The integral shall be easier to evaluate. Also, remember that convolution is a linear operator, so scale the integral accordingly. Also, lim(0→k) ∫(t^n)dt= [t^(n+1)]/(n+1) evaluated for limits 0 to k.