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Chapter 8 – Further Applications of Integration

Chapter 8 – Further Applications of Integration. 8.2 Area of a Surface of Revolution. Area of a Surface Revolution. A surface of revolution is formed when a curve is rotated about a line. Rotation about the x -axis. If f is positive and has a continuous derivative, we define the surface

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Chapter 8 – Further Applications of Integration

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

  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

  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-axisas 8.2 Area of a Surface of Revolution

  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-axisas 8.2 Area of a Surface of Revolution

  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

  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

  7. Book Resources • Video Examples • 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

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

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