Integrating to find Volume (different from the other guy)

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SUMMARY

The discussion focuses on calculating the volume of a solid formed by rotating the area between the curves y=11 and y=x+28/x around the line x=-4 using the shell method. The user expresses confusion regarding the setup of the integral, particularly in determining the shell radius and the region of integration. Clarification on these points is essential for correctly applying the shell method to solve the problem.

PREREQUISITES
  • Understanding of the shell method for volume calculation
  • Familiarity with integral calculus
  • Knowledge of curve equations and their graphical representation
  • Ability to identify regions bounded by curves
NEXT STEPS
  • Review the shell method for volume of revolution
  • Study how to set up integrals for rotating regions about vertical lines
  • Practice finding the shell radius for various curves
  • Explore examples of volume calculations using y=11 and y=x+28/x
USEFUL FOR

Students studying calculus, particularly those focusing on volume of solids of revolution, and educators looking for examples of applying the shell method in real problems.

CB4
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Ok so I'm doing my online homework and I came across this problem:

"Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line.

y=11, y=x+28/x

about x=-4"


So I attempted to use the shell method to solve this equation but I get confused on how to set up my integral. I don't really know how to tackle the region I'm integrating about (x=-4).
 
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Are you having trouble finding the shell radius, or something else? If you could be more specific, or show your work, it would be easier to help.
 

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