ok, so I was going over the polar and spherical integrations and determined I had forgotten a few things.

a polar rectangle area = r dt * dr ; I had forgotten why to include the "r".

but in spherical I can get an r^2 but I dont get why there is a sin(t) involved :/

dr * r dt * r dp is what I was thinking; but it turns out the formula has it as r sin(t) dp and I cant see why. Any ideas?

Question

ok, so I was going over the polar and spherical integrations and determined I had forgotten a few things.

a polar rectangle area = r dt * dr ; I had forgotten why to include the "r".

but in spherical I can get an r^2 but I dont get why there is a sin(t) involved :/

dr * r dt * r dp is what I was thinking; but it turns out the formula has it as r sin(t) dp and I cant see why.  Any ideas?

amistre64 · Answer

the controls on OS seem a little sluggish tonight

turingtest · Answer

do you know/remember about the whole jacobian thing?
that can derive those formulas

amistre64 · Answer

i havent put forth an real effort to disect thru a jacobian yet; it goes in one ear and out the other at the moment

anonymous · Answer

you could calculate the jacobian for this change of variables:$$x=r\sin\phi\cos\theta $$$$y=r\sin\phi\sin\theta$$$$z=r\cos\phi$$

anonymous · Answer

bah, didnt see you last post, nvm lol

turingtest · Answer

can I be annoying and just shoot you a link; it's a pain to type out... http://tutorial.math.lamar.edu/Classes/CalcIII/ChangeOfVariables.aspx try to keep that formula between your ears this time ;)

amistre64 · Answer

of read thru the Pauls stuff last night, but wasnt getting what i was after

turingtest · Answer

examples 2 and 5 answer your exact questions

amistre64 · Answer

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i have an exact question?  lol