Question

The value of L[1] is​

Answer 1

Answer:

By Laplace Transform

Value of L{1} is : 1/s

Answer 2

$\displaystyle \sf{L[1] = \frac{1}{s} }$

Given :

$\sf L[1]$

To find :

The Laplace transform

Concept :

Laplace transform :

The Laplace transform of f(t), denoted by L{f(t)} and defined as :

$\displaystyle \sf{ L\{f(t)\} =\int\limits_{0}^{\infty} e^{-st} f(t)\, dt}$

Solution :

Step 1 of 2 :

Define Laplace transform

The Laplace transform of f(t), denoted by L{f(t)} and defined as :

$\displaystyle \sf{ L\{f(t)\} =\int\limits_{0}^{\infty} e^{-st} f(t)\, dt}$

Step 2 of 2 :

Find Laplace transform of 1

$\displaystyle \sf{ L[1] }$

$\displaystyle \sf{ =\int\limits_{0}^{\infty} e^{-st} .1\, dt}$

$\displaystyle \sf{ = \frac{e^{-st}}{ - s} \bigg| _{0}^{\infty} }$

$\displaystyle \sf{ = 0 + \frac{1}{s} }$

$\displaystyle \sf{ = \frac{1}{s} }$