Converting to Cylindrical Coordinates for Triple Integration

In summary, the conversation discusses converting a triple integral to cylindrical coordinates but struggling with converting the bounds. The suggestion is to focus on the xy-plane and sketch the region bounded by the limits of the integrals. The given integral expression in Latex is also provided for reference.
  • #1
TheAntithesis
14
0
I don't want the answer, just a little help getting there.
The question asks to integrate this: Triple integral

I'm thinking to convert it to cylindrical but I have no idea how to convert the bounds. I can convert the actual expression z/sqrt(x^2+y^2) into cylindrical no problem. If I had some picture as to what the bounds look like then I might be able to get somewhere. Any help would be greatly appreciated.
 
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  • #2
Forget about z for now. Sketch the region bounded by the limits of the integrals in the xy-plane.
 
  • #3
In Latex:

[tex]\int_0^2 \int_0^{\sqrt{4-x^2}} \int_0^{(x^2+y^2)/2} \frac{z}{\sqrt{x^2+y^2}}\ dz\, dy\, dx[/tex]
 

1. What is a triple integral?

A triple integral is a mathematical calculation that is used to find the volume of a three-dimensional region in space. It involves integrating a function of three variables over a three-dimensional region.

2. How is a triple integral different from a double integral?

A triple integral is similar to a double integral, but it involves integrating a function of three variables over a three-dimensional region, whereas a double integral involves integrating a function of two variables over a two-dimensional region.

3. What is the purpose of using a triple integral?

The purpose of using a triple integral is to find the volume of a three-dimensional object or region. It is commonly used in fields such as physics, engineering, and mathematics to solve problems involving three-dimensional shapes and volumes.

4. What are the steps involved in solving a triple integral?

The steps involved in solving a triple integral include: 1) determining the limits of integration for each variable, 2) setting up the integrand (the function being integrated), 3) evaluating the integral using appropriate integration techniques, and 4) interpreting the result in the context of the problem.

5. Are there any real-world applications of triple integrals?

Yes, triple integrals have many real-world applications in fields such as physics, engineering, and economics. Some examples include calculating the mass and center of mass of a three-dimensional object, finding the electric flux through a three-dimensional region, and determining the probability of a particle's position in quantum mechanics.

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