Question
Part 2 of 2
Let R be the region bounded by
generated when R is revolved about the line
Set up the integral that gives the volume of the solid using the shell method. Select the correct choice below and fill
in the answer boxes to complete your choice.
(Type exact answers.)
A.
B.
The volume of the solid is
(Type an exact answer.)
Let R be the region bounded by
generated when R is revolved about the line
Set up the integral that gives the volume of the solid using the shell method. Select the correct choice below and fill
in the answer boxes to complete your choice.
(Type exact answers.)
A.
B.
The volume of the solid is
(Type an exact answer.)
Ask by Graham Wood. in the United States
Mar 29,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The volume of the solid is
Solution
To find the volume of the solid generated when the region R is revolved about the line
The shell method formula for finding the volume of a solid is given by:
where:
-
is the radius of the shell, -
is the height of the shell, -
and are the limits of integration.
In this case, the region R is bounded by
Therefore, the integral that gives the volume of the solid using the shell method is:
So, the correct choice is:
B.
B.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Beyond the Answer
To find the volume of the solid generated by revolving the region
Volume Integral Setup:
The height of the shell is given by the function
The height of the shell is given by the function
The complete setup for the integral is:
Final Volume Calculation:
To find the exact volume, you would evaluate the integral:
To find the exact volume, you would evaluate the integral:
To combine these fractions:
So, the volume of the solid is
