# Fundamental Mathematics/Calculus/Integration

## Integration

Mathematics operation on a continuous function to find its area under graph . There are 2 types of integration

${\displaystyle \int f(x)dx=F(x)+C}$

Where ${\displaystyle F}$ satisfies ${\displaystyle F'(x)=f(x)}$

Suppose ${\displaystyle f}$ is a continuous function on ${\displaystyle [a,b]}$ and ${\displaystyle \Delta x={\frac {b-a}{n}}}$ . Then the definite integral of ${\displaystyle f}$ between ${\displaystyle a}$ and ${\displaystyle b}$ is

${\displaystyle \int \limits _{a}^{b}f(x)dx=\lim _{n\to \infty }A_{n}=\lim _{n\to \infty }\sum _{i=1}^{n}f(x_{i}^{*})\Delta x}$

Where ${\displaystyle x_{i}^{*}}$ are any sample points in the interval ${\displaystyle [x_{i-1},x_{i}]}$ and ${\displaystyle x_{k}=a+k\cdot \Delta x}$ for ${\displaystyle k=0,\dots ,n}$ .}}