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Find the mass of a ball B given by "x^2+y^2+z^2≤a^2" if the density at any point is proportional to its distance from the z-axis using cylindrical coordinates So is the density equal to K*sqrt(x^2+y^2), or K*r?

Using triple integral of f(rcosθ, rsinθ, z)*r*dz*dr*dθ) I got the following: the triple integral of K*r^2dz*dr*dθ, and the limits for the integral w/ respect to z being from -sqrt(a^2-x^2-y^2) to sqrt(a^2-x^2-y^2), which becomes -sqrt(a^2-r^2) to sqrt(a^2-r^2), limits w/ respect to r being from 0 to a and w/ respect to theta from 0 to 2*pi.

Doing it I find the integral very hard to integrate because I can't do u-subsititon with two r^2's.

Am I doing anythign wrong? Thanks in advance.

Using triple integral of f(rcosθ, rsinθ, z)*r*dz*dr*dθ) I got the following: the triple integral of K*r^2dz*dr*dθ, and the limits for the integral w/ respect to z being from -sqrt(a^2-x^2-y^2) to sqrt(a^2-x^2-y^2), which becomes -sqrt(a^2-r^2) to sqrt(a^2-r^2), limits w/ respect to r being from 0 to a and w/ respect to theta from 0 to 2*pi.

Doing it I find the integral very hard to integrate because I can't do u-subsititon with two r^2's.

Am I doing anythign wrong? Thanks in advance.

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