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!