## Definite Integration

One of the uses of integration is to find the area between a curve and the x-axis.
These areas are found be evaluating a definite integral. When anti-differentiating the result is a function. When evaluating a definite integral the answer is a number.

### Defiinite Integrals

A definite integral is calculated by integrating a function between two values, called the limits of integration. These two values are substituted into the integrated function and the difference taken.

The formula is: f(x) dx = F(b) − F(a) where F(x) is an anti-derivative of f(x)

This complicated looking formula is easier to use than it looks. It simply means doing the following:

 Method Example Evaluate (x2 + 3) dx Step 1 Integrate the function = Step 2 Substitute the values 2 and 1 = - Step 3 Evaluate Note that the constant of integration c is not shown as it would be eliminated when subtracting.

### Definite Integration by Substitution

If the method of integration used is substitution, the limits of integration are changed to those of the variable used in the substitution.

Example  