Question

Find Laplace transform of exp(t)​

Answer 1

Step-by-step explanation:

The Laplace Transform of a function y(t) is defined by

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if the integral exists. The notation L[y(t)](s) means take the Laplace transform

of y(t). The functions y(t) and Y(s) are partner functions. Note that Y(s) is indeed only a function of s since the definite integral is with respect to t.

Examples

Let y(t)=exp(t). We have

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The integral converges if s>1. The functions exp(t) and 1/(s-1) are partner

functions.

Let y(t)=cos(3t). We have

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The integral converges for s>0. The integral can be computed by doing