Suppose that a person has a lottery ticket from which she will win $X$ dollars, where $X \sim\mathrm{ Unif} (0,4)$. Suppose her utility function is $U(x) = x\alpha$ for $x \geq 0$ and $0$ otherwise, where $\alpha > 0$ is some fixed constant. For how many dollars is she willing to sell the ticket (i.e., what is $E[U(X)]$)?
I am little confused how to start this problem?
Is it going to be $\int_0^1 x*\alpha dx$?