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Inverse Laplace Transform Calculator
Enter the function into input box and click calculate button to calculate Laplace's inverse by using inverse Laplace transform calculator
Inverse Laplace Transform Calculator
Inverse Laplace Transform calculator is used to evaluate the inverse Laplace transform of a given function. This Inverse Laplace calculator will give the result with steps.
What is meant by inverse Laplace transform?
The inverse Laplace transform is the method to transform a given function into the function of time. Inverse Laplace transform is a mathematical technique for taking the inverse of a Laplace transform function. Inverse Laplace transform is also known as inverse Laplace or inverse Laplace transformation. It is denoted as L-1(f(t)).
If F(s) is the Laplace transform of the function is f(t). then the inverse transformation is defined as an operator which maps f(t) to F(s). Symbolically it is written as
f(t) = L-1(F(s)), F(s) = L(f(t))
Formula:
The inverse Laplace transformation in the integral form is given as:
$$L^{-1}\left[F\left(s\right)\right]=\frac{1}{2\pi i}\int _{\left(a-i∞\right)}^{\left(a+i∞\right)}F\left(s\right)\:e^{ts}\:ds$$
Examples of Inverse Laplace Transform
We have to discuss some functions to find the Laplace inverse to understand the mathematical way how to calculate it.
Example 1:
Find the inverse Laplace transformation of the function 9/(s-3) + 1/(13s+5) +9/(s5).
Solution:
Step 1: We have to first convert the given terms in the standard form to apply the formula:
L-1(s) = 9/(s-(-3)) – 1/13(s-5/13) +9 (4!)/4! (s4+1)
Step 2: Now using the formula 1/s-n = en and 1/sn+1 = tn
L-1(s) = 9e-3t- e5/13/13 + 9/24 t4
Example 2:
Find the Laplace inverse transformation of the function s/(s2+7)+1/s2.
Solution:
Step 1: Taking the inverses separately we have
L-1(s/(s2+7)) = cos(71/2t)
L-1 (1/s2) = t
Step 2: Now combine the terms together, we have
L-1 (s/(s2+7)+1/s2)=cos(71/2t) + t
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