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# Using the integral definition of the Laplace transform to compute a function

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(a) Use the integral definition of the Laplace transform to compute (FUNCTION1)
(b) A function g(t) has the transform (FUNCTION2). Use transform properties to compute the following. Express each in simplest form:
i) (FUNCTION3)
ii) (FUNCTION4)
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https://brainmass.com/math/integrals/integral-definition-laplace-transform-compute-function-26959

#### Solution Preview

(1) Integral definition of Laplace transform:

L[f(t)] = Integral (from t = 0 to inf.)[exp(-st)f(t)dt]

= Integral (from t = 0 to inf.)[exp(-st)*t^2*dt]

= Integral (from t = 1 to 2)[exp(-st)*t^2*dt]

Use Integration by parts (or use the formula from ...

#### Solution Summary

This solution is provided in 262 words. It uses step-by-step equations using the Laplace transform and transform properties to find the integral definition of a function.

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