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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)
    (See attachment for full question).

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    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.