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Differential EquationsEasyLaplace II: Steps, Impulses & Convolution

Laplace II: Steps, Impulses & Convolution · Easy problem

Compute the convolution (u(t−1)∗e−t)(t)=∫0tu(τ−1) e−(t−τ) dτ\bigl(u(t-1)*e^{-t}\bigr)(t)=\displaystyle\int_0^t u(\tau-1)\,e^{-(t-\tau)}\,d\tau at t=3t=3. Give an exact answer.