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