I'm trying to prove a simple example of MGF for $E[x]$ for a simple RV with uniform distribution over range $[0,10]$ but not sure where I'm getting stuck:
$A(t) = E[e^{tx}] = \int_{0,10}e^{tx}dx/10$ *note Riemann Sum not Lebesgue
My understanding is then you take the derivative $d/dt$ of $A(t)$ but when doing so I get:
$ (e^{10t} - 1)/t - (e^{10t} - 1)/10t$ How does this equal $5$ which is $E[x]$ given the above definition of $x$ being uniformly distributed from $[0,10]$?