Area of Surfaces of Revolution | Calculus 2 Lesson 7 - JK Math

How to Calculate Area of Surfaces of Revolution (Calculus 2 Lesson 7)

In this video we look at how to use definite integrals to calculate the area of surfaces of revolution, which are surfaces formed by revolving a curve about an axis, such as the x-axis or y-axis. We derive the formula used to calculate this area, and then look at example problems of using the formula.

This series is designed to help students understand the concepts of Calculus 2 at a grounded level. No long, boring, and unnecessary explanations, just what you need to know at a reasonable and digestible pace, with the goal of each video being shorter than the average school lecture!

Calculus 2 requires a solid understanding of calculus 1, precalculus, and algebra concepts and techniques. This includes limits, differentiation, basic integration, factoring, equation manipulation, trigonometric functions, logarithms, graphing, and much more. If you are not familiar with these prerequisite topics, be sure to learn them first!

Video Chapters:
0:00 Determining the Formula
6:42 Area of a Surface of Revolution Formulas
8:49 Example 1 - f(x)=x^3 from x=0 to x=1 around x-axis
19:38 Example 2 - f(x)=x^2 from x=0 to x=sqrt(2) around y=axis
30:04 Outro

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[AK_]

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[MelodicMurder]

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[ydm]

thank you soo muchh broo, the playlist really helps me a lot in studying for finals

[gabygarcia]

Hi! Great video! But in the book Calculus: Early Transcendentals the formula that they use for SA is is the integral from a to b 2pi f(x) sqrt(1+f'(x)^2)dx. Is the f(x) the same thing as r(x)? Because for the example at 19:40 they would not be the same thing I think?

[BilalAhmed-onkd]

why not multiply it by dx instead of l just like in volume