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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.

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