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Mathematical Expression Editor
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We practice choosing a method for computing volume when none is specified.
(Spring 2016 Final Exam) Find the volume of the solid generated by revolving the
region in the first quadrant bounded by , , and about the line .
Using as the slicing variable, slices are
to the axis . This alignment corresponds to the
method. (Expand to continue.)
The height of a shell is
and the radius is
Therefore
(Fall 2012 Final Exam) The region in the -plane bounded by and the -axis for
is rotated about the -axis. What is the volume of the resulting solid of
revolution?
Using as the slicing variable, slices are
to the axis . This alignment corresponds to the
method. (Expand to continue.)
The outer radius of a disk is
and the inner radius is
Therefore
Find the volume of the solid generated by revolving the region in the first quadrant
bounded on the left by , on the right by , and below by about the axis
.
To carry out the calculation as efficiently as possible, the
-variable should be used as the variable for slicing. (Expand to continue.)
Using as the slicing variable, slices are
to the axis . This alignment corresponds to the
method. (Expand to continue.)
The height of a shell is
and the radius is
Therefore
Start typing the name of a mathematical function to automatically insert it.
(For example, "sqrt" for root, "mat" for matrix, or "defi" for definite integral.)
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Start typing the name of a mathematical function to automatically insert it.
(For example, "sqrt" for root, "mat" for matrix, or "defi" for definite integral.)