I am having trouble with this triple integral. It seems so easy, but I keep getting stuck at the same spot, and I'm not sure where I am going wrong.
Evaluate the triple integral over E, where E is bound by the sphere (x^2) + (y^2) + (z^2) = 9 in the first octant. The density function is given by:
exp(sqroot((x^2) + (y^2) + (z^2))).
So by using spherical coordinates I get the following as my limits:
0 < theta < 2pi, 0 < phi < pi/4, 0 < rho < 3. Is this right?
After changing variables, I get (exp(rho))*(rho^2)*sin(phi) for the density. Is that right? After this, I'm not sure where to go, since integrating (exp(rho))*(rho^2)*sin(phi) w/r/t rho doesn't seem like the easiest thing to do. Maybe I need to switch my order of integration?
Any ideas? Thanks.