# Triple integral in cylindrical coordinates

• norbellys
In summary, the person is trying to solve a triple integral using cylindrical coordinates and has made a mistake with the limits. They are reminded that the element of volume in cylindrical coordinates is ##r~dz~ dr~ d\theta## and they had forgotten the ##r## term.
norbellys
1. Homework Statement
I am trying to solve a triple integral using cylindrical coordinates. This is what I have to far . But I think I have choosen the limits wrong.

## The Attempt at a Solution

[/B]

norbellys said:
1. Homework Statement
I am trying to solve a triple integral using cylindrical coordinates. This is what I have to far . But I think I have choosen the limits wrong.

## The Attempt at a Solution

[/B]

Assuming your first line is correct, your change to cylindrical coordinates is almost correct. The only change I see you need is to remember that the element of volume in cylindrical coordinates is ##r~dz~ dr~ d\theta##. You forgot the ##r##.

LCKurtz said:
Assuming your first line is correct, your change to cylindrical coordinates is almost correct. The only change I see you need is to remember that the element of volume in cylindrical coordinates is ##r~dz~ dr~ d\theta##. You forgot the ##r##.
yes that was what I was missing !

## 1. What is a triple integral in cylindrical coordinates?

A triple integral in cylindrical coordinates is a mathematical tool used to calculate the volume of a three-dimensional region in space. It involves integrating a function over a region defined by three variables: radius, angle, and height.

## 2. How do you set up a triple integral in cylindrical coordinates?

To set up a triple integral in cylindrical coordinates, you need to first identify the region of integration and express its boundaries in terms of the cylindrical coordinates (ρ, φ, z). Then, you need to determine the function to be integrated and write it in terms of these coordinates. Finally, you can set up the integral using the formula: ∭f(ρ, φ, z) dρdφdz.

## 3. What are the advantages of using cylindrical coordinates for triple integrals?

Using cylindrical coordinates for triple integrals can simplify the calculation process for certain types of three-dimensional regions, such as cylinders, cones, and spheres. It also allows for easier visualization of the region and can make the integration limits easier to determine.

## 4. How do you convert a triple integral in Cartesian coordinates to cylindrical coordinates?

To convert a triple integral from Cartesian coordinates to cylindrical coordinates, you can use the following equations: ρ = √(x² + y²), φ = arctan(y/x), z = z. Then, you can replace the x, y, and z variables in the integral with the corresponding ρ, φ, and z expressions.

## 5. What are the physical applications of triple integrals in cylindrical coordinates?

Triple integrals in cylindrical coordinates have various applications in physics and engineering, such as calculating the mass, center of mass, and moment of inertia of a three-dimensional object. They are also used in electromagnetism to calculate electric and magnetic fields in cylindrical symmetry problems.

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