Where to use polar (cylindrical coor.) in double and triple integrals

[Amaelle]

Homework Statement

Where to use polar (cylindrical coordinates) in double and triple integration

Relevant Equations

y=rsin(theta)
x=rcos(thera)

where the region of integration is the cube [0,1]x[0,1]x[0,1]

my question is where can we use the polar coordinate? is it only usable if the region of integration looks like a circle regardless of the function inside the integral? (if yes it means that using this kind of transformation is wrong in our case)
many thanks in advance

 

[pasmith]

The point of transformations is to either simplify the domain or to simplify the integrand.

If the domain is already $[0,1]^3$ then it's as simplified as it can be and you should stick with those coordinates.

 

[Amaelle]

thanks a lot !

 

[Kaura]

You could use polar coordinates to evaluate a cube, however it would require a piece wise integration since the sharp edges of the cube have discontinuous derivatives.

If a function is smooth, such as a sphere or ellipse, then polar coordinates can often times be ideal.

Many times it is simply preference and intuition as to the manner of the problem.

 

[Amaelle]

Thanks a lot that was the answer i was looking for