Chapter 7.1, Problem 7P

Program Plan Intro

Program Description: Purpose of problem is to obtain the Laplace transformation described in the given figure.

Summary introduction:Program will use the definition of Laplace transform of function $F\left(s\right)$ for all $t\ge 0$ and is defined as,

  $L\left\{f\left(t\right)\right\}={\displaystyle \underset{0}{\overset{\infty }{\int }}{e}^{-st}f\left(t\right)dt}$ ..........(1)

Here, the improper integral will converges for all values of $s$ .

The linearity theorem of the Laplace transform for all $s$ such that the functions $f$ and $g$ both exists is defined as,

  $L\left\{af\left(t\right)+bg\left(t\right)\right\}=aL\left\{f\left(t\right)\right\}+bL\left\{g\left(t\right)\right\}$