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Laplace Transform Calculator
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Laplace Transforms Calculators (known as laplace transform calculator with steps or laplace calculator) are used to creates the very easy to resolve the linear variant equations with given primary conditions. The Calculator is laplace transformation online are mostly used in the integral transform. The Laplace Transforms have several major applications in the math, science, manufacturing and probability theory. It solve functions into with Fourier transform. It is a laplace solver or laplace rechner. It also used for resolving the differential and essential equations.

Laplace Transform Definition

If f(t) $\in$ R defined $\forall$ t $\geq$ 0, then the Laplace Transform of f(t) is given by
L[f(t)] = $\int_{0}^{\infty}$ e-st f(t) dt
By the definition of Laplace Transform
L[f(t)] = $\int_{0}^{\infty}$ e-st f(t) dt = F(s)
Here, F(s) = $\int_{0}^{\infty}$ e-st f(t) dt = shift operator.
Standard Laplace Transform Formulas

L[tn] = $\frac{n!}{s^{n + 1}}$
L[eat] = $\frac{1}{s - 1}$
L[Sin at] = $\frac{a}{s^2 + a^2}$
L[Cos at] = $\frac{s}{s^2 + a^2}$
L[Sinh at] = $\frac{a}{s^2 - a^2}$
L[Cosh at] = $\frac{s}{s^2 - a^2}$
L[t sin at] = $\frac{2as}{(s^2 + a^2)^{2}}$
L[t cos at] = $\frac{s^{2} - a^{2}}{(s^2 + a^2)^{2}}$
L[eat tn] = $\frac{n!}{(s - a)^{n+1}}$
L[t e-t] = $\frac{1}{(s + 1)^{2}}$
You can see a default function with their function variable and transform variable given below. When u click on "Calculate", Laplace transform of the given function can be calculated by applying the appropriate formula given in the standard Laplace transform formulas given above.

## Steps for Laplace Transform Calculator

Step 1 :

Observe the given function f(t).

Step 2 :

Find the Laplace transform of the given function by using the formula

L[f(f)] = $\int_{0}^{\infty}$ e-st f(t) dt = F(s)

Use the standard results of Laplace transform.

## Laplace Transform Problems

1. ### Find laplace transform of [Sin 2t] ?

Step 1 :

L[Sin 2t] = ?

Step 2 :

We know that L[Sin at] = $\frac{a}{s^2 + a^2}$

So, L[Sin 2t] = $\frac{2}{s^2 + 2^2}$
= $\frac{2}{s^2 + 4}$

L[Sin 2t] = $\frac{2}{s^2 + 4}$

2. ### Find laplace transform of Cos 4t ?

Step 1 :

L[Cos 4t] = ?

Step 2 :

We know that L[Cos at] = $\frac{s}{s^2 + a^2}$

So, L[Cos 4t] = $\frac{s}{s^2 + 4^2}$
= $\frac{s}{s^2 + 16}$

L[Cos 4t] = $\frac{s}{s^2 + 16}$