Chapter-6-p-2.pdf - Chapter 6 Applications of Definite Integrals 1 2 3 4 5 6 Volumes using Cross-Sections Solids of Revolution The Disk Method Solids of

Chapter-6-p-2.pdf - Chapter 6 Applications of Definite...

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Chapter 6. Applications of Definite Integrals 1. Volumes using Cross-Sections 2. Solids of Revolution: The Disk Method 3. Solids of Revolution: The Washer Method 4. Volume using Cylindrical Shells 5. Arc Length 6. Area Surfaces of Revolution HKU MATH1851
2 1. Volume using Cross-Sections
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4 If the two solid have the same height and cross-sectional areas, then they have same volume .
5 2. Solids of Revolution: The Disk Method Volume by disks for rotation about the x-axis y-axis The solid is generated by rotating a plane region about an axis, and all cross-section is disk.
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8 3. Solids of Revolution: The Washer Method Volume by Washers for rotation about the x-axis y-axis The solid is generated by rotating a plane region about an axis and some cross-section is annulus.
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11 4. Volume using Cylindrical Shells The solid is now sliced with cylinders. (In previous sections, it is sliced in disks/annuli.)
12 Volume using Cylindrical Shells - Explanation
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15 5. Arc Length Justification:
16 Example
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18 6. Area Surfaces of Revolution Justification:
19 More details:
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21 Example

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