Another thread about integration!

Soldato
Joined
11 May 2006
Posts
5,786
I'm really confused on this question (no seriously I am!) and would really appreciate some input.

A solid hemisphere H of radius a has density depending on the distance p from the centre of the base disc and given by 2a-p. Write down the mass of the hemisphere as a triple integral in: spherical polar, cylindrical polar and cartesian coordinates.

Now, I have no problem creating the triple integrals in the three coordinate systems but what confuses me is the density and mass functions. For example in the cartesian form, would the integral simply be:

int(int(int(2*a-z))).dz.dy.dx ?

Does the p simply mean movement along the z-axis or am I missing something? Will the same thing apply to the other coordinate systems? Sorry if this is a really silly question, but I really appreciate some clarification on this. :confused:
 
That makes a lot more sense! :) So the 2a-p density function is given in spherical coordinates. Hence when writing it in cylindrical and cartesian coordinate systems, would I be correct in using 2a-sqrt(r^2+z^2) and 2a-sqrt(x^2+y^2+z^2) respectively?
 
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