- #1
MAins
- 18
- 0
1.
"Find the mass of part of the solid sphere x^2 + y^2 + z^ 2 ≤ 25 in the 1st octant x ≥ 0, y ≥ 0, z ≥ 0 where mass density is f (x, y, z ) = (x^2 + y^2 + z^2 )^3/2 ."
3.
These problems are really stumping me! I need somebody to work it out/explain it to me! What will the limits of integration be for the following question? What do i integrate? I know I need to transform it to spherical coordinates... but beyond that I'm lost.
I know it's a triple integral:
m = ∫∫∫(x^2 + y^2 + z^2)^3/2 dzdydx
transforming to spherical co-ordinates:
0 ≤ rho ≤ 5
0 ≤ theta ≤ ? (how do I figure this out?)
0 ≤ phi ≤ ? (ditto)
dzdydx = rho^2 sinphi drho dphi dtheta
What does f (x, y,z) transform to and how do I figure it out?
"Find the mass of part of the solid sphere x^2 + y^2 + z^ 2 ≤ 25 in the 1st octant x ≥ 0, y ≥ 0, z ≥ 0 where mass density is f (x, y, z ) = (x^2 + y^2 + z^2 )^3/2 ."
3.
These problems are really stumping me! I need somebody to work it out/explain it to me! What will the limits of integration be for the following question? What do i integrate? I know I need to transform it to spherical coordinates... but beyond that I'm lost.
I know it's a triple integral:
m = ∫∫∫(x^2 + y^2 + z^2)^3/2 dzdydx
transforming to spherical co-ordinates:
0 ≤ rho ≤ 5
0 ≤ theta ≤ ? (how do I figure this out?)
0 ≤ phi ≤ ? (ditto)
dzdydx = rho^2 sinphi drho dphi dtheta
What does f (x, y,z) transform to and how do I figure it out?