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Chapter 08Applications of Integrals

0108.01Derivatives of Integral Functions
0208.02Net Change and Area Between Curves
0308.03Volume by Slicing
0408.04Solids of Revolution: Disk/Washer Method
0508.05Solids of Revolution: Shell Method
0608.06Average Value of a Function
0708.07Arc Length
0808.08Surface Area of Solids of Revolution
0908.09Tricky Integrals
1008.10Calculating Work
1108.11Center of Mass
1208.12Other Physical Applications

Chapter 08 · Applications of Integrals

0108.01Derivatives of Integral Functions
0208.02Net Change and Area Between Curves
0308.03Volume by Slicing
0408.04Solids of Revolution: Disk/Washer Method
0508.05Solids of Revolution: Shell Method
0608.06Average Value of a Function
0708.07Arc Length
0808.08Surface Area of Solids of Revolution
0908.09Tricky Integrals
1008.10Calculating Work
1108.11Center of Mass
1208.12Other Physical Applications

Topics / 08 Applications of Integrals

08.08

Surface Area of Solids of Revolution

Spin a curve around an axis: each tiny piece of arc sweeps out a thin band of area 2π · radius · length.

About 15 minutes

You'll learn to

→Set up surface area integrals around either axis
→Combine the radius with the arc length element
→Check the formula on spheres and cones

← 08.07 Arc Length 08.09 Tricky Integrals →

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