Joe P. answered • 11/24/19
NASA Alum, math, physics, logic, project, test-prep, and homework help
You have to look for symmetry. If things look Cartesian in one dimension but radial otherwise, use cylindrical. If things radial in more than just two dimensions, go spherical.
Example paths for line integrals:
x = cos(t), y = sin(t), z = et: use cylindrical since there is radial symmetry in the xy-plane and z shooting off exponentially.
x = cos(t), y = sin(t)cos(t), z = sin2(t): use spherical since this has spherical symmetry.
Also, after doing a lot of these you will build a pattern-noticing ability to spot coordinate that just ending being more convenient.
Do you have a specific example that you are thinking about?
Ashley P.
Thank you very much for the answer! Yeah, to be specific how do we distinguish between which should be used from cylindrical and polar coordinates for evaluating the line integral s 1) -[(x^2+y-4) dx + 3xy dy] And Can you please provide examples of the type of the above, for each where spherical and polar coordinates are used for evaluating line integrals? Many thanks!11/24/19