If there are limit values indicated on your integral, you are looking to find a definite integral. This means that these values will be used to find a numeric answer rather than a function.

This is done in the following way, where the values for a and b are substituted as x-values into your indefinite integral:

Solving definite integrals

- Find the indefinite integral (without +C)

2. Fill in: F(b) − F(a)
(integral x = b) − (integral x = a)

### 5.2.1 Area

**Area between a curve and the x-axis**

**DB 5.5****Area between two curves**

Using definite integrals you can also find the areas enclosed between curves:

Finding areas with definite integrals.

Let y = x

^{3}− 4x^{3}+ 3x Find the area from x = 0 to x = 3.- Find the x-intercepts: f (x) = 0

x^{3} − 4x^{3} + 3x = 0, using the GDC: x = 0 or x = 1 or x = 3

3. Setup integrals and integrate

4. Add up the areas (and remember areas are never negative!)

Alternatively, use the calculator to find areas

In this case, the area is 3.083