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Comparison of Volume Methods

Comparison of Volume Methods. MAT152. Disks/Washers and Shells. Shells Multiply the definite integral by TWO pi Involves no squaring. Disks and Washers Multiply the definite integral by ONE pi Involves squaring. Disks/Washers and Shells. Shells

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Comparison of Volume Methods

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  1. Comparison of Volume Methods MAT152

  2. Disks/Washers and Shells Shells • Multiply the definite integral by TWO pi • Involves no squaring Disks and Washers • Multiply the definite integral by ONE pi • Involves squaring

  3. Disks/Washers and Shells • Shells • The representative unit is parallel to the axis of revolution. • Disks/Washers • The representative unit is perpendicular to the axis of revolution.

  4. Revolving around the x-axis • Shells • When revolving an enclosed region around the x-axis, write the integrand in terms of Y and integrate with respect to Y. • Disks/Washers • When revolving an enclosed region around the x-axis, write the integrand in terms of X and integrate with respect to X.

  5. Revolving around the y-axis • Shells • When revolving an enclosed region around the y-axis, write the integrand in terms of X and integrate with respect to X. • Disks/Washers • When revolving an enclosed region around the y-axis, write the integrand in terms of Y and integrate with respect to Y.

  6. How much toilet paper is on those rolls? Finding the answer: Volumes Also making some reasonable assumptions

  7. What to do first… • Think about putting a roll of toilet paper on a set of axes: 2 f(x) 1 g(x) 1 0

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