triple integral

queenstudy

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

I like Serena

"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.

resolvent1

No, you have to use the change of variables formula.

queenstudy

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

I like Serena

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.

queenstudy

so let me ask this one last time , if you dont 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

I like Serena

It depends on how the problem is stated exactly.

queenstudy

I have any domain D and i want to express the triple integral using cartesian coordinates??

I like Serena

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.

queenstudy

no i mean triple integral
yes it is triple integral does it make a difference???????????????

I like Serena

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.

queenstudy

but polar coordinates are a special case used to facilitate our calculations in the x and y axis that what our proffessor said

I like Serena

So you could for instance start out in polar coordinates and convert them to cartesian coordinates, since that is what is requested.

resolvent1

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.

queenstudy

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