# Laplace Transform of a Function over a specified interval.

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Khaled Mohamed on 7 Feb 2020
Edited: Walter Roberson on 7 Feb 2020
I want to find the laplace transform of a function. for example cos(t) but with a condition such that 0<t<4.
Vladimir Sovkov on 7 Feb 2020
You mean, you want something like ? Then, just estimate it as the integral, either numerically (function "integral") or symbolically (function "int"). The other way is to define your function as the symbolic piece-wise one (equal to what you want within [0,4] and zero outside) and use the function "laplace".

Walter Roberson on 7 Feb 2020
Edited: Walter Roberson on 7 Feb 2020
syms t
lowerbound = 0; upperbound = 4;
F = heaviside(t-lowerbound) * heaviside(upperbound-t) * cos(t)
laplace(F)
The boundary conditions might not be exactly what you want so you might need to toss in some dirac()

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