Can we use the disk method in this integral?

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The discussion centers on the application of the disk method for a specific integral involving a sphere and a paraboloid. The user questions whether the disk method is appropriate, noting that the sphere extends deeper into the paraboloid than the intersection point at x=-1. A participant clarifies that the formula 2πρ dρ represents a ring, not a disk, suggesting that the user's calculations are valid. The conversation emphasizes the importance of understanding the geometric implications of the shapes involved in the integral. Overall, the consensus is that the disk method may not be suitable due to the geometry of the problem.
Amaelle
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Homework Statement
look at the image
Relevant Equations
cylindrical coordinates
Goodd day, I have a question regarding an exercice I have already posted
1613466709445.png

Bvu was very nice and provided this darwing
1613466770802.png

I already have the solution
1613466832087.png
But y question is :
can we use the disk method? because as you can see even though the intersection was at x=-1 the sphere goes deep into the paraboloid until x=-sqrt(2)?
so maybe the only way is to caluculate is to
1613468607815.png

Many thanks in advance!
 
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2\pi\rho d\rho is not disk but ring. So I think your calculation is OK.
 

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