Use the Convolution Theorem to prove the time integration formula: if L[f(t)] = F(s), then L[integral from 0 to t of f(tau)*dtau] = 1/s*F(s) where L[….

Use the Convolution Theorem to prove the time integration formula:if L[f(t)] = F(s), then L[integral from 0 to t of f(tau)*dtau] = 1/s*F(s)where L[.] is the laplace transform

L(f (t)) = F (s)tt∞´´´f (τ )dτLf (τ )dτ = e−st0 =t´ t´ f (τ )dτ 0 f (τ )dτ ´ ´ 0 0∞ e−st dt∞ −st e dt −0 ∞´ ´ dte−st dt f (t)dt 0 =0 0 0 t´…