Shell method
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Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the y axis.
1. y=x. Line goes from (0,0) to to (2,2). Picture shows a thin yellow rectangle going from about x=1.5 vertical to the y=x line.
2) y=sq. root of x. Line goes from (0,0) to to (4,2). Picture shows a thin yellow rectangle going from about x=2.5 vertical to the y=sq. root of x line.
5) y=x^2, y=0,x=2
7) y=x^2, y=4-x^2
9) y=4-x^2, x=0, y=4
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Solution Summary
There are several problems using the shell method to find the volume of a solid created by revolving an equation around the axis.
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