Definite Integrals

Integration

Integration can be used to find areas, volumes, central points and many useful things. But it is often used to find the area under the graph of a function like this:
The area can be found by adding slices that approach zero in width: And there are Rules of Integration that help us get the answer.

The symbol for "Integral" is a stylish "S"
(for "Sum", the idea of summing slices):

After the Integral Symbol we put the function we want to find the integral of (called the Integrand),

and then finish with dx to mean the slices go in the x direction (and approach zero in width).

A Definite Integral has start and end values: in other words there is an interval [a, b].

a and b (called limits, bounds or boundaries) are put at the bottom and top of the "S", like this:


Definite Integral (from a to b)		Indefinite Integral (no specific values)