Hi, just having some issues with this problem...

Integral over the unit sphere of (x^2 + y^2 - 2z^2) dA

I changed all the x, y, z into spherical coordinates (using a and b for the angles) with r = 1

Calculated the determinant to be (sin a)

I set up my work like this:

double integral of (sin a) ((sin a)^2 - 2(cos a)^2) db * da

taking b from 2pi to 0, and a from pi to 0

Skipping the work I did (I presume I did something wrong in the setup...)

My answer came out to be

2pi * ((cos pi)^3 - cos pi - (cos 0)^3 + cos 0)

But this gives me zero. I don't understand...

The answer given is

(2pi/3) * ((1 + a^2)^(3/2) - 1)

I suppose I don't understand something because I'm not sure where this a is supposed to come from//be since its obviously not the same as what I did.

Help appreciated thanks!