Question

need some help setting up bounds in a spherical triple integral.

Answer 1

Let \(W\) be the solid of the first octant bounded above by \(z=\sqrt{x^2+y^2}\) and on the sides by \(x^2+y^2=1\). Assume the solid has mass density given by the function \(\rho(x,y,z)=z+\sqrt{x^2+y^2}\). Set up a triple integral in spherical coordinates.

Answer 2

So I know that my function is going to be \[\iiint_T(\rho\cos\phi+\rho\sin\phi)\rho^2\sin{\phi}\,d\rho\,d\phi\,d\theta \]

Answer 3

and I can see how to get \[\int^{1/sin\phi}_0\] for the first one. But how the heck do I figure out the other two limits of integration?

Answer 4

Does that make sense?
Sorry, I got interrupted...

Answer 5

not really, I don't see how you can get that without graphing it!

Answer 6

Ok, well I graphed it in my head first, and then I drew it for you......