Laplace Transform Calculator

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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


  • 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


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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