You might like to read Introduction to Integration first!
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 is found by adding slices that approach zero in width (dx):
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) |
We find the Definite Integral by calculating the Indefinite Integral at a, and at b, then subtracting: