For the functions f(t) = et and g(t) = e-t, defined on 0 < t <...

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For the functions f(t) = et and g(t) = e-³t, defined on 0 < t < ∞, compute f * g in two different ways: a. By directly evaluating the integral in the definition of f * g. t (f*g) (t) = √² b. By computing L−¹ {F(s)G(s)} where F(s) = L {f(t)} and G(s) = L {g(t)}. (f*g)(t) = L−¹ {F(s)G(s)} = L−¹{| = dw = help (formulas) For the functions f(t) = et and g(t) = e-³t, defined on 0 < t < ∞, compute f * g in two different ways: a. By directly evaluating the integral in the definition of f * g. t (f*g) (t) = √² b. By computing L−¹ {F(s)G(s)} where F(s) = L {f(t)} and G(s) = L {g(t)}. (f*g)(t) = L−¹ {F(s)G(s)} = L−¹{| = dw = help (formulas)