1) Using the definition integral transform to calculate the Laplace transform of a) f(t) = 10e-4t b) f(t) = t² 2) Use the Laplace transform tables to find the Laplace transform of each function below: a) f(t)=-10 cos 2t b) f(t)=4e3 sin(t - 45°)u(t - 45°) c) f(t) = 4te-3t 3) Given that f(t) = 4e-3(-4), of Laplace a) Find [] by differentiating f(t) and then using the Laplace transform tables dt b) Find using the theorem for differentiation C dt c) Repeat a) and b) for the case that f(t) = 4e-3(-4)u(t - 4)