Laplace transformation t^(3/2)

[jrsweet]

Homework Statement

Just a quick question concerning a Laplace transformation...
Find the Laplace transform of the following function:
f(t)=10t^3/2-e^(-7t)

Homework Equations

The Attempt at a Solution

I wasn't sure what to do with the t^3/2 so I just followed the formula for t^1/2 and I got this:

(10pi^(3/2))/(2s^5/2)-(1/(s+7))

Is there anything wrong with this?

 

[Mark44]

t^1/2 and t^3/2 are different functions, so it should be expected that their Laplace transforms would be different.
L{t^{k - 1}} = $\Gamma$(k)/s^k, where $\Gamma$ represents the gamma function.

$$\Gamma(z)~=~\int_0^{\infty} t^{z - 1}~e^{-t}dt$$
Hope that helps.