Calc2
posted by chelsea on .
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.

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