Plane Areas

Example 1
Find the area enclosed by r = 2a sin² θ.
 

Example 3
Find the area bounded by the curve x = y² + 2y and the line x = 3.
 

Example 2
Find the area bounded by the curve a² y = x³, the x-axis and the line x = 2a.
 

Example 1
Find the area bounded by the curve y = 9 - x² and the x-axis.
 

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

1. by using a horizontal element (called strip) of area, and
2. 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.
 

Using Horizontal Strip