consider this following triple integral
1/(x^2+y^2+z^2)dxdydz
bounded above by sphere z=(9-x^2-y^2)^1/2 and below by the cone z=(x^2+y^2)^1/2
what i have done:
z=Pcospi
P^2=x^2+y^2+z^2
9=x^2+y^2+z^2
P=0 to 3
pi=0 to pi/4
theta=0 to 2pi
is this the correct range?
I think his P is supposed to be the spherical coordinate ρ, so his limits are correct. naspek, don't forget the spherical dV element.I would first equate the z's to find that [itex]x^{2}+y^{2}=9/2[/itex], then this means that the radius is [itex]3/\sqrt{2}[/itex] and i think that you limits are: [itex]3/\sqrt{2}\leqslant r\leqslant 3[/itex] and all your limits are okay.