I have a random variable X and a set A in the real numbers such that Pr[X in A] > 0.

Let E[X given X in A] = (1/Pr[X in A])*integral of xfX(x)dx for X continuous.

I have that X ~ N(0,1) and I need to find E[X given X > 2].

So, I think I need (1/Pr[X > 2])*(integral of xfX(x) from 2 to infinity)dx where fX(x) is the marginal density function. How do I do this integration? It seems overly complicated. I believe the marginal density function is the expression with 1/sqrt(2*pi) etc. and I don't know how to integrate it with x in front.

Any help is appreciated.