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Area, Volume, and Arc Length

Area, Volume, and Arc Length

Example 1

Let R be our favorite region.

Use the shell method to write an integral expression for the volume of the solid obtained by rotating R around the line

x = 2

Example 2

Let R be our favorite region.

Use the shell method to write an integral expression for the volume of the solid obtained by rotating R around the line

y = 1

Example 3

Let R be the region in the first quadrant bounded by the graph y = x2, the y-axis, and the line y = 4. Use the shell method to write an integral expression for the volume of the solid obtained by rotating R around

the y-axis

Example 4

Let R be the region in the first quadrant bounded by the graph y = x2, the y-axis, and the line y = 4. Use the shell method to write an integral expression for the volume of the solid obtained by rotating R around

the line x = -1

Example 5

Let R be the region in the first quadrant bounded by the graph y = x2, the y-axis, and the line y = 4. Use the shell method to write an integral expression for the volume of the solid obtained by rotating R around

the x-axis

Example 6

Let R be the region in the first quadrant bounded by the graph y = x2, the y-axis, and the line y = 4. Use the shell method to write an integral expression for the volume of the solid obtained by rotating R around

the line y = 5

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