limits of integration

Example 6 | Plane Areas in Rectangular Coordinates

Example 6
Find each of the two areas bounded by the curves y = x3 - 4x and y = x2 + 2x.
 

Example 3 | Plane Areas in Rectangular Coordinates

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

Example 2 | Plane Areas in Rectangular Coordinates

Example 2
Find the area bounded by the curve a2 y = x3, 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 - x2 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...

  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

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