Laplace transforms A powerful tool in solving problems in engineering and physics is the Laplace transform. Given a function f(t), the Laplace transform is a new function F(s) defined by where we assume then s is a positive real number. For example, to find the Laplace transform oj f(t)= e?t, the following improper integral is evaluated using integration by parts: Verify the following Laplace transforms, where a is a real number.

Problem 76ELaplace transforms A powerful tool in solving problems in engineering and physics is the Laplace transform. Given a function f(t), the Laplace transform is a new function F(s) defined by where we assume then s is a positive real number. For example, to find the Laplace transform of f(t)= et, the following improper integral is evaluated using integration by parts:Verify the following Laplace transforms, where a is a real number. f(t) = 1 F(s) = Answer; Step-1 of 3; Given , the laplace transform is a new function F(s) defined by . Now , we have to prove f(t) = 1 F(s)...