Question

@JamesJ,@TuringTest

can you explain me this

Answer 1

What part do you not understand?

Answer 2

I meant ds

Answer 3

\[x=r\cos\theta\]\[y=r\sin\theta\]\[z=z\]Then you need the Jacobian of the transformation... or you can just memorize that when switching to cylindrical or polar coordinates you pick up an extra r in the differential.

Answer 4

check out example 2:
http://tutorial.math.lamar.edu/Classes/CalcIII/ChangeOfVariables.aspx
try the same trick for cylindrical coordinates and you will find that you get the same thing i.e. the extra r