A spherical cloud of gas of radius 3km is more dense at the center that toward the edge, at a distance p km from the center the density is d(p) = 3 - p, write an integral representing the total mass of the cloud and evaluate it.
My problem is not evaluating the integral it is setting it up.
Clearly the best option is a triple integral in spherical coordinates.
/pi / 2pi / 3
| | | d(p)p^2 sin(x) dp dy dx
| | |
/0 /0 /0
Here is my problem, I've tried with d(p) = 3-p like the problem states and I get a very strange answer, the homework solution uses p - 3, and I dont see why that make this change. Please help.