# limits of integration

## Example 6 | Plane Areas in Rectangular Coordinates

## Example 3 | Plane Areas in Rectangular Coordinates

**Example 3**

Find the area bounded by the curve x = y^{2} + 2y 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 = 2a.

## 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.