Can I use polar coordinates in a triple integral?

In summary, when solving a triple integral problem in cartesian form, it is possible to use polar coordinates as a special case to simplify calculations. However, if the problem specifically asks for the domain to be expressed in terms of cartesian coordinates, then the change of variables formula must be used to convert from polar to cartesian coordinates. This allows the integral to be solved in terms of cartesian coordinates.
  • #1
queenstudy
101
0
if i am being asked to write the domain of integration in a triple integral problem in a cartesian form , may i used polar coordinates to express instead of x and y? thank you
 
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  • #2
"Cartesian" form in a triple integral means x, y, and z.
"Polar" is another form (meaning r, theta, and phi).
So I would conclude that you're not supposed to use polar coordinates.
 
  • #3
No, you have to use the change of variables formula.
 
  • #4
I like Serena said:
"Cartesian" form in a triple integral means x, y, and z.
"Polar" is another form (meaning r, theta, and phi).
So I would conclude that you're not supposed to use polar coordinates.

but from what i took in class polar coordinates are r and theta only let me explain my problem more.
if i have a disk of radius 1 covering the (xOy) axis and i want to to integration, it is better to use polar coordinates than cartesian coordinates , but my proffesor told me that polar coordinates are part of cartesian by by saying that x=rcosθ and y=rsinθ
your thoughts please and thank you very much for helping me out
 
  • #5
Yes, if you want to do a (double) integration on a circular disk, it's usually best to use polar coordinates to calculate the result.

But that is not what is asked in your problem statement.
Your problem statement asks to define the domain (of a circular disk I presume?) in terms of cartesian coordinates (meaning x and y).

After you have done that, it may be expedient for a next part of your problem to convert to polar coordinates to actually calculate the integral.
 
  • #6
so let me ask this one last time , if you don't mind , when i am askled to find any integration by cartesian coordinates , may i use the polar coordinates or not?? and thank you very very much serena
 
  • #7
It depends on how the problem is stated exactly.
 
  • #8
I have any domain D and i want to express the triple integral using cartesian coordinates??
 
  • #9
queenstudy said:
I have any domain D and i want to express the triple integral using cartesian coordinates??

Then you have no choice.
It has to be x and y.

Btw, I presume you meant double integral?
Otherwise your problem would be 3-dimensional.
 
  • #10
I like Serena said:
Then you have no choice.
It has to be x and y.

Btw, I presume you meant double integral?
Otherwise your problem would be 3-dimensional.

no i mean triple integral
yes it is triple integral does it make a difference?
 
  • #11
A triple integral in cartesian coordinates requires you to use x, y, and z.

It means that you would typically integrate over a sphere or a cylinder, which you can do with x, y, and z.
 
  • #12
but polar coordinates are a special case used to facilitate our calculations in the x and y-axis that what our proffessor said
 
  • #13
So you could for instance start out in polar coordinates and convert them to cartesian coordinates, since that is what is requested.
 
  • #14
queenstudy said:
so let me ask this one last time , if you don't mind , when i am askled to find any integration by cartesian coordinates , may i use the polar coordinates or not?? and thank you very very much serena

Yes, you can use polar coordinates.

What your professor told you to use is the change of variables formula, by setting x = r sin(theta), etc. This defines a transformation from xyz space to r-theta-z space - thus the integral over, say, a cylinder in xyz space is equal to the integral over a box in r-theta-z space. The integral in r-theta-z space uses cartesian coordinates in that space.

Or in other words, the integral in terms of angles and radii (polar coords) becomes an integral in terms of cartesian coords.
 
  • #15
resolvent1 said:
Yes, you can use polar coordinates.

What your professor told you to use is the change of variables formula, by setting x = r sin(theta), etc. This defines a transformation from xyz space to r-theta-z space - thus the integral over, say, a cylinder in xyz space is equal to the integral over a box in r-theta-z space. The integral in r-theta-z space uses cartesian coordinates in that space.

Or in other words, the integral in terms of angles and radii (polar coords) becomes an integral in terms of cartesian coords.

thank very much the i will use polar coordinates to facilitate my calculations
 

1. What is a triple integral?

A triple integral is an extension of a regular integral in one variable, to three variables. It calculates the volume under a three-dimensional surface in space.

2. What is the domain of a triple integral?

The domain of a triple integral is the region in three-dimensional space over which the integral is being evaluated. It is usually represented by a three-dimensional shape such as a cube, sphere, or cylinder.

3. How is the domain of a triple integral determined?

The domain of a triple integral is determined by the limits of integration for each variable. These limits can be found by considering the boundaries of the three-dimensional shape that represents the domain.

4. Can the domain of a triple integral be a non-rectangular shape?

Yes, the domain of a triple integral can be any three-dimensional shape, including non-rectangular ones. In this case, the limits of integration for each variable will be determined by the boundaries of the shape.

5. What are some applications of triple integrals?

Triple integrals are used in many fields of science, such as physics, engineering, and mathematics. Some common applications include calculating the volume of a solid, finding the center of mass of an object, and determining the probability of an event in probability theory.

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