1. Chapter 8 – Further Applications of Integration
8.2 Area of a Surface of Revolution
8.2 Area of a Surface of Revolution
Erickson

2. Area of a Surface Revolution
A surface of revolution is formed when a curve is rotated about a line.
8.2 Area of a Surface of Revolution
Erickson

3. Rotation about the x-axis
If f is positive and has a continuous
derivative, we define the surface
area of the surface obtained by
rotating the curve y = f (x),
a ≤ x ≤ b, about the x-axis as
8.2 Area of a Surface of Revolution
Erickson

4. Rotation about the y-axis
If f is positive and has a continuous
derivative, we define the surface
area of the surface obtained by
rotating the curve x = g(y),
c ≤ y ≤ d, about the y-axis as
8.2 Area of a Surface of Revolution
Erickson

5. Example 1 – pg. 550
Find the area of the surface obtained by rotating the curve about the x-axis. 7. 9.
10.
8.2 Area of a Surface of Revolution
Erickson

6. Example 2 – pg. 550
The given curve is rotated about the y-axis. Find the area of the resulting surface
13.
14.
16.
8.2 Area of a Surface of Revolution
Erickson

7. Book Resources Video Examples More Videos Wolfram Demonstrations
Example 2 – pg. 540
Example 3 – pg. 541
Example 4 – pg. 542
More Videos
Arc Length Parameter
Wolfram Demonstrations
Surface Area of a Solid of Revolution
7.7 Approximation Integration
Erickson

8. Web Resources http://youtu.be/-j2eKo84Ef8 http://youtu.be/Jxf_XeKsiyY
8.2 Area of a Surface of Revolution
Erickson