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Triple integral 
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#1
Dec2311, 09:26 AM

P: 102

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



#2
Dec2311, 10:13 AM

HW Helper
P: 6,189

"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
Dec2311, 11:44 AM

P: 24

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



#4
Dec2311, 02:56 PM

P: 102

Triple integral
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
Dec2311, 03:07 PM

HW Helper
P: 6,189

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
Dec2311, 03:14 PM

P: 102

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



#8
Dec2311, 03:32 PM

P: 102

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



#9
Dec2311, 03:50 PM

HW Helper
P: 6,189

It has to be x and y. Btw, I presume you meant double integral? Otherwise your problem would be 3dimensional. 


#10
Dec2311, 03:58 PM

P: 102

yes it is triple integral does it make a difference??????????????? 


#11
Dec2311, 03:59 PM

HW Helper
P: 6,189

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
Dec2311, 04:03 PM

P: 102

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



#13
Dec2311, 04:07 PM

HW Helper
P: 6,189

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



#14
Dec2311, 04:51 PM

P: 24

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 rthetaz space  thus the integral over, say, a cylinder in xyz space is equal to the integral over a box in rthetaz space. The integral in rthetaz 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
Dec2411, 06:06 AM

P: 102




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