Definition of Integral

Let $ f$ be a continuous function on the interval $ [a,b]$. The definite integral is just the signed area between the graph of $ f$ and the $ x$ axis:

Definition 2.1.2 (Definite Integral)   The definite integral of $ f(x)$ from $ a$ to $ b$ is

$\displaystyle \int_{a}^{b} f(x) dx = \lim_{n\to\infty}\left( \sum_{i=1}^n f(x_i^*) \Delta x \right).

Properties of Integration:

There are many other properties.

William Stein 2006-03-15