 # Laplace Transform Calculator

To use Laplace Transform calculator, enter the function, and click calculate button

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## Laplace Transform Calculator

Laplace transform calculator is used to perform mathematical operations related to Laplace transforms. This Laplace calculator will transform the function in a fraction of a second.

## What is Laplace Transform?

Laplace transformation is a technique that allows us to transform a function into a new shape where we can understand and solve that problem easily. It maps a real-valued function into a function of a complex variable. It is very useful to solve differential equations. It is mostly used to transform the analysis of the data values.

### Formula of Laplace Transform

The formula of the Laplace transformation is if the domain is given as.

 L{f(s)} = ∫0∞ [f(t)e-st ] dt Where  f(t) is the function of time. f(s) is the function of frequency. ∫0∞ is the notation of improper integral.

## Example of Laplace Transform

Find the Laplace transform of the function f(t)= 3t- 3t+ 3

Solution:

Step 1: Write the function in the Laplace notation

L(3t- 3t+ 3)

Step 2: Apply the transformation separately on each term, we have

= L(3t6) - L(3t2) + L(3)

Step 3: Now take the constant outside form the transformation.

= 3L(t6) - 3L(t2) + 3L(1)

Step 4: Now using the formula (tn)= n!/sn+1

L(t6) =6! /s6+1

L(t6) =720 /s7

L(t2) =2! /s2+1

L(t2) =2 /s3

L(1) = 0! / s0+1

L(1) =1/ s

Step 5: Now put the values in the formula

= 3L(t6) - 3L(t2) + 3L(1)

= 3(720 /s7) - 3(2 /s3) + 3(1/s)

= 2160/s7- 6/s3+ 3/s

Hence the Laplace transformation is 2160/s- 6/s+ 3/s

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