Chapter 7.1, Problem 35P

Program Plan Intro

Program Description: Purpose of the problem is to obtain the Laplace transform of the function $f\left(t\right)=\cos kt$ using integral ${\displaystyle \int e^{ax}}\cos bxdx=\frac{e^{ax}}{a^2+b^2}\left(a\cos bx+b\sin bx\right)+C$ .

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 $s$ .