Expectation of a non negative random variable

For any non negative continuous random variable having distribution function $F(X)$ we have the followings:

1. $E[X]={\int }_0^{\mathrm{\infty }}Pr[X>t]dt$

2. $E[X^r]=r{\int }_0^{\mathrm{\infty }}{t}^{r-1}Pr[X>t]dt$

3. $E[\min (X,T)]=T-{\int }_0^{\mathrm{\infty }}F(T)𝑑t$

4. where $T$ is a constant.