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Example 8

The region R under the curve y = 1/x from 1 to ∞ is rotated about the x-axis, forming a solid of revolution. Find the volume of this solid (Figure 8.5.4).

08_exp-log_functions-255.gif

Figure 8.5.4

The volume is given by the improper integral

08_exp-log_functions-256.gif

Then

08_exp-log_functions-257.gif

Thus the solid has volume π.


Last Update: 2006-11-16