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.
 

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

Problem integrating with the disk method
    • Calculus and Beyond Homework Help
Replies
5
Views
962
Problem figuring out the surface of integration
    • Calculus and Beyond Homework Help
Replies
2
Views
809
Integration by filaments or integration by strate?
    • Calculus and Beyond Homework Help
Replies
7
Views
1K
Can't Find a Correct Method to Integrate \int (t - 2)^2\sqrt{t}\,dt?
    • Calculus and Beyond Homework Help
Replies
9
Views
725
Calculate this Integral around the Circular Path using Green's Theorem
    • Calculus and Beyond Homework Help
Replies
3
Views
273
Problem with a double integral
    • Calculus and Beyond Homework Help
Replies
4
Views
870
Integration problem using inscribed rectangles
    • Calculus and Beyond Homework Help
Replies
14
Views
244
Verify Green's Theorem in the given problem
    • Calculus and Beyond Homework Help
Replies
10
Views
441
Solve ##\int\frac{e^{-x}}{x^2}dx## and ##\int \frac{e^{-x}}{x}dx##
    • Calculus and Beyond Homework Help
Replies
7
Views
706
Question about a double integral region
    • Calculus and Beyond Homework Help
Replies
5
Views
930

Hot Threads

Recent Insights

Back
Top