Answer to Question #343122 in Differential Equations for Tobias Felix

Question

Find the Laplace transforms of the following function:

5. L{t^4}

Answer 1

$${\cal L}\{f\}(s)=\int_0^{\infty}f(t)e^{-st}dt$$

$${\cal L}\{t^4\}(s)=\int_0^{\infty}t^4e^{-st}dt$$

$$=\frac{d^4}{ds^4}\int_0^{\infty}e^{-st}dt=\frac{d^4}{ds^4}(1/s)=\frac{24}{s^5}$$