Calc2

Let f(t) be a function defined for all values of t. The Laplace Transform of f(t) is defined by: F(s)= �ç[∘,�‡](e^-st(f(t))dt). If the improper integral exists, Find the Laplace Transform for F(t)=t^2.

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  1. well, we know that L{1} = 1/s

    and, we know from our handy table of transforms that

    L{t^n f(t)} = (-1)^n F(n)(s)

    so,

    L{t^2} = 2/s^3

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