Volume: The Disk Method

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Section 7.2

• Volume The Disk Method

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Examples (from mathdemos.org)
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Examples (from mathdemos.org)
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Examples (from mathdemos.org)
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Examples (from mathdemos.org)
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Examples (from mathdemos.org)
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Formulas Disk Method (about x axis)
Note Function must be of the form y
_____ and a and b are in terms of x values
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Formulas Disk Method (about y axis)
Note Function must be of the form x
_____ and c and d are in terms of y values
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Formulas Washer Method (about x axis)
Note Function must be of the form y
_____ and a and b are in terms of x values
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Formulas Washer Method (about y axis)
Note Function must be of the form x
_____ and c and d are in terms of y values
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Washer Method Revolving about a Line

• R(x) Line - Farthest Graph
• r(x) Line - Nearest Graph

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1. Set up and evaluate the integral that gives
the volume of the solid formed by revolving the
region about the x-axis (similar to p.465 1-5)
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2. Set up and evaluate the integral that gives
the volume of the solid formed by revolving the
region about the x-axis (similar to p.465 1-5)
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3. Set up and evaluate the integral that gives
the volume of the solid formed by revolving the
region about the y-axis (similar to p.465 7-9)
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4. Set up and evaluate the integral that gives
the volume of the solid formed by revolving the
region about the y-axis (similar to p.465 7-9)
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5. Find the volumes of the solids generated by
revolving the regions bounded by the graphs of
the equations about the given lines (similar to
p.465 11-13)

1. the x-axis
2. the y-axis
3. the line x 8
4. the line x 10

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6. Find the volume of the solid generated by
revolving the region bounded by the graphs of the
equations about the line y 6 (similar to p.465
15-17)
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7. Find the volume of the solid generated by
revolving the region bounded by the graphs of the
equations about the line x 5 (similar to p.465
19-21)
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8. Find the volume of the solid generated by
revolving the region bounded by the graphs of the
equations about the x-axis (similar to p.465
23-29)
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9. Find the volume of the solid generated by
revolving the region bounded by the graphs of the
equations about the x-axis (similar to p.465
33-35)