Can we use the disk method in this integral?

In summary, the disk method can only be used for finding the volume of solids of revolution with circular cross-sections. The formula for using the disk method in an integral is V = &pi;&int;<sub>a</sub><sup>b</sup>(f(x))<sup>2</sup>dx, where a and b are the limits of integration and f(x) is the function defining the cross-sectional area. It can be used for both solids of revolution about the x-axis and y-axis, with the only difference being the orientation of the cross-sectional area. The radius of the disks is determined by the function defining the cross-sectional area, and it cannot be used for irregularly shaped objects.
  • #1
Amaelle
310
54
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!
 
Physics news on Phys.org
  • #2
[tex]2\pi\rho d\rho [/tex] is not disk but ring. So I think your calculation is OK.
 

Related to Can we use the disk method in this integral?

1. Can the disk method be used to find the volume of any solid?

Yes, the disk method can be used to find the volume of any solid with a circular cross section. It is a commonly used method in calculus to calculate volumes of solids of revolution.

2. What is the formula for using the disk method in an integral?

The formula for using the disk method in an integral is V = π ∫ (r(x))^2 dx, where r(x) is the radius of the cross section at a given point.

3. Can the disk method be used for solids with non-circular cross sections?

No, the disk method can only be used for solids with circular cross sections. For solids with non-circular cross sections, other methods such as the shell method may be used.

4. What are the limitations of using the disk method?

The disk method is limited to finding the volume of solids with circular cross sections. It also requires the function to be integrated to be continuous and have a known upper and lower bound.

5. How does the disk method differ from the washer method?

The disk method and the washer method are both used to find the volume of solids of revolution. The difference lies in the shape of the cross section - the disk method uses circular cross sections while the washer method uses annular (ring-shaped) cross sections.

Similar threads

  • Calculus and Beyond Homework Help
Replies
5
Views
980
  • Calculus and Beyond Homework Help
Replies
2
Views
835
  • Calculus and Beyond Homework Help
Replies
7
Views
1K
  • Calculus and Beyond Homework Help
Replies
9
Views
765
  • Calculus and Beyond Homework Help
Replies
3
Views
414
  • Calculus and Beyond Homework Help
Replies
4
Views
891
  • Calculus and Beyond Homework Help
Replies
14
Views
382
  • Calculus and Beyond Homework Help
Replies
10
Views
539
  • Calculus and Beyond Homework Help
Replies
7
Views
762
  • Calculus and Beyond Homework Help
Replies
5
Views
961
Back
Top