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.

Question

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.

Steve · Answer

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

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.