Question

Find the Laplace transform of the function f(t)=a+bt+ct²using the definition

Answer 1

The Laplace transform, is an integral transform that converts a function of a real variable (often time) to a function of a complex variable (complex frequency) .

The Laplace transform of a function f(t), defined for all real numbers t ≥ 0, is the function F(s), which is a unilateral transform defined by

where s is a complex number frequency parameter.

f(t)=a+bt+ct²

= ( a+bt+ct² )*e^(-st) dt

=(a*e^(-st) dt )+(bt * e^(-st) dt)+(ct^2*e^(-st) dt)

=a/s + b/s^2 +2*c/s^3

The Laplace transform of the function f(t)=a+bt+ct²using the definition is a/s + b/s^2 +2*c/s^3,

where s is complex valued variable .