Hey mcleja.
Basically you need to go from cartesian to polar co-ordinates in three dimensions. Take a look at this wiki entry:
List of common coordinate transformations - Wikipedia, the free encyclopedia
Hi all,
I would like some help with a parameterization. The parameterization is as follows:
S is the surface of a sphere with center at (6, −2, 4) and radius 6, V is the volume bounded by S.
parameterize the volume V, using the parameters (r, θ, φ).
How do I do this problem?
I don't even know where to begin.
Any help much appreciated.
Hey mcleja.
Basically you need to go from cartesian to polar co-ordinates in three dimensions. Take a look at this wiki entry:
List of common coordinate transformations - Wikipedia, the free encyclopedia
Now you need to get your limits in terms of the polar co-ordinates.
The limits for a sphere are easy in polar space since r is from 0 to 6 and the angles are just exhaustive (from 0 to 2pi and 0 to pi if I recall correctly).
Since all the limits are separate (i.e. they all are independent and don't depend on other variables) the integration is a lot easier which is why you do this in polar space and not cartesian space.