Expected Value of a PDF

$\mathbb{E}(X)=\int xf(x)dx$

$\mathbb{E}(X^2)=\int x^{2}f(x)dx$

We call this a moment

$\mathbb{E}(X^n)=\int x^{n}f(x)dx$

If values are discrete

$\mathbb{E}(g(X))=\sum (g(x)p(x))$