integrals in latex code example

Example 1: latex integral

$ \int_{a}^{b} x^2 \,dx $

Example 2: latex sum

Inside text: $\sum_{n=1}^{\infty} 2^{-n} = 1$
On its own line: $$\sum_{n=1}^{\infty} 2^{-n} = 1$$

Example 3: integral latex

integral 
\[ \int_{a}^{b} x^2 \,dx \]

Example 4: integral latex

$\int_0^{2a}{\cos(x)dx}$