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Laplace transform properties


									           Laplace transform properties
Laplace transform properties

Laplace functions can easily be solved with help of Laplace properties. Laplace
transform properties are given below: 1. Linearity: All the Laplace function fallow
linearity property as: kx1 (t) +mx2 (t) ⇐⇒kx1(s) + mx2(s).

This process is reversible Delay by t: Whenever function is delayed by t then its
Laplace transforms decrease exponentially x(t-T)=X(S)e-st Multiply by t:
Whenever we multiply any function by ‘t’ its Laplace transform we divided it by ‘t’
with negative sign.

 tx(t)=-dX(S)/ds Divide by t: Whenever we divide any function by ‘t’ its Laplace
transform multiplied by ‘t’ with negative sign. x(t)/t=-sx(s) Differentiate in t:
Whenever we differentiate the function its Laplace transform multiplied by a
variable d/dx(x(t)) =sX(s).
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Relationship to Laplace Transform to other transform

Laplace transform rechecks a function into its instance. Relationship of Laplace
transform to other transform can be given as: Laplace transform performs on
the density of functi...

Evaluating Improper Integrals

posted on: 21 Feb, 2012 | updated on: 27 Feb, 2012
Integration can be called as improper integration if interval of integration is not
finite or integrated function is not continuous in interval and for evaluation of
improper integration we use following steps - Step 1: First of all assume any
variable for indefinite value of interval like - ∫01 1 dx , then let t = 0 because at
0, 1 is not continuous .
     x                                 x Step 2: After assuming variable make limit
at value of constant like - lim ∫t1 1 dx
t->0 x Step 3: After this calculate limit - lim ∫t1 1 dx = lim [ - 1 ]t1 = lim [-1 + 1 ]
= -1
t->0 x        t->0 x2         t->0     t2 These three steps are used for evaluating
improper integrals .

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