Moments about the mean of a uniform distribution

Question

I really don't know what needs to be completed here, because I don't understand the parameters of alpha and beta:

Show that if a random variable has a uniform density with the parameters alpha and beta, the $r$th moment about the mean is $\frac{1}{r+1}\left(\frac{\beta-\alpha}{2}\right)^r$ and zero otherwise.

Answer 1

$\alpha$ is the lower end of the uniform distribution while $\beta$ is the upper end. All possible values between them are equally likely

Hint:

$$E[X]=\frac{\alpha+\beta}{2}$$

since the mean is also the mid point, so you want to calculate

$$E\left[\left(X-E[X]\right)^r\right]=\dfrac1{\beta-\alpha}\int_\alpha^\beta \left(x-\frac{\alpha+\beta}{2}\right)^r \, dx$$