horizontal strip

Situation
Given the parabola 3x² + 40y – 4800 = 0.
 

Part 1: What is the area bounded by the parabola and the X-axis?
A. 6 200 unit²
B. 8 300 unit²
C. 5 600 unit²
D. 6 400 unit²
 

Part 2: What is the moment of inertia, about the X-axis, of the area bounded by the parabola and the X-axis?
A. 15 045 000 unit⁴
B. 18 362 000 unit⁴
C. 11 100 000 unit⁴
D. 21 065 000 unit⁴
 

Part 3: What is the radius of gyration, about the X-axis, of the area bounded by the parabola and the X-axis?
A. 57.4 units
B. 63.5 units
C. 47.5 units
D. 75.6 units
 

Example 2
Find the volume generated when the area in Example 1 will revolve about the y-axis.
 

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

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