# limits of integration

## Example 6 | Plane Areas in Rectangular Coordinates

**Example 6**

Find each of the two areas bounded by the curves *y* = *x*^{3} - 4*x* and *y* = *x*^{2} + 2*x*.

## Example 3 | Plane Areas in Rectangular Coordinates

**Example 3**

Find the area bounded by the curve *x* = *y*^{2} + 2*y* and the line *x* = 3.

## Example 2 | Plane Areas in Rectangular Coordinates

**Example 2**

Find the area bounded by the curve *a*^{2}*y* = *x*^{3}, the *x*-axis and the line *x* = 2*a*.

## Example 1 | Plane Areas in Rectangular Coordinates

**Example 1**

Find the area bounded by the curve *y* = 9 - *x*^{2} and the *x*-axis.

## Plane Areas in Rectangular Coordinates | Applications of Integration

There are two methods for finding the area bounded by curves in rectangular coordinates. These are...

- by using a horizontal element (called strip) of area, and
- by using a vertical strip of area.

The strip is in the form of a rectangle with area equal to length × width, with width equal to the **differential element**. To find the total area enclosed by specified curves, it is necessary to sum up a series of rectangles defined by the strip.