I have $f(x)=x/8$ for $0<x<4$. I'm asked (in a practice test) to find $E[x\mid x \ge 2]$.

My solution, based on something our TA showed us but I didn't fully understand, is as follows:

I took the integral $\int\_0^2 x(x/8)\,dx$ divided by the integral $\int\_0^2 x/8\,dx$. I got $4/3$.

Is this correct? If so, can someone explain the intuition behind this method?