Question

Laplace transform of a function f(t) is expressed by formula​

Answer 1

Answer:

In order to transform a given function of time f(t) into its corresponding Laplace transform, we have to follow the following steps: First multiply f(t) by e-st, s being a complex number (s = σ + j ω). Integrate this product w.r.t time with limits as zero and infinity

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Answer 2

Answer:

Laplace transform of a function f(t) is expressed by formula​:

$Laplace transform of f(t)= L[f(t)]=F(s)=\int_{0}^{\infty} f(t) \cdot e^{-s t} d t when t \geq 0$

Step-by-step explanation:

• A Laplace transform of function f (t) in a time domain, where t is the real number greater than or equal to zero, is given as F(s),

                                    $F(s)=\int_{0}^{\infty} f(t) \cdot e^{-s t} d t when t \geq 0$

where there 's' is the complex number in frequency domain .i.e. s = σ+jω

The above equation is considered as unilateral Laplace transform equation.

• When the limits are extended to the entire real axis then the Bilateral Laplace transform can be defined as
•                               $F(s)=\int_{-\infty}^{\infty} f(t) \cdot e^{-s t} d t when t \geq 0$