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. Use increasing limits of integration.
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. Use increasing limits of integration.
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 Barrett Mills. in the United States
Mar 29,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The volume of the solid is
Solution
Let the region be
When revolving
- The radius of a typical shell is the horizontal distance from
to : - The height of the shell is the value of the function:
- The differential thickness is
.
Thus, the volume element is
The integral giving the volume is
Evaluating the integral:
Thus, the correct choice is B with the integral
and the volume of the solid is
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Extra Insights
To set up the integral for the volume using the shell method, we first identify the elements involved when revolving around the line
-
The correct integral to compute the volume is
. Since we need to express everything in terms of , we know that , leading to . -
The volume of the solid generated is calculated as follows:
So, the completed choice with the integral setup is:
A.
And the volume of the solid is:
Thus, the exact answer could be further simplified based on evaluating the integral limits.
