# Arc Length and Surface Area

Taught by Houston
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Meets NCTM Standards:
Lesson Description:

Length of an arc y = f(x), a < x < b. Area of a surface of revolution.

Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more information on videos, resources, and lessons at http://online.math.uh.edu/HoustonACT/videocalculus/index.html.

• How do you find arc length or length of a curve in Calculus?
• What is the formula for arc length?
• What is the length of the arc y = x^2 between 0 and 2?
• How do you find the length of the arc y = sin x between 0 and pi?
• How can you use Simpson's Rule to find arc length?
• How do you find the area of a surface of revolution?
• How do you find the area of an arc that was revolved?
• What is arc-length differential?
• What is surface area differential?
• What is the formula for the area of a surface if you rotate about the x-axis?
• What is the formula for the area of a surface if you rotate about the y-axis?
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This lesson explains finding the arc length of a function, also called the length of a curve. It goes through the derivation of the arc length formula and then uses the formula in several examples. Then, you will learn how to find the area of a surface of revolution. There is a summary at the end that sums up the formulas and concepts from the videos.