Question

Let W be the region between concentric spheres centered at the origin of radii a and b, a < b. Consider the triple integral
dV/(x^2 + y^2 + z^2)^(3/2) Convert this integral to spherical coordinates.
:
(a) Convert this integral to spherical coordinates.

Answer 1

for spherical coordinates r=sqrt(x^2+y^2+z^2)

Answer 2

so the the triple integral would be dV/(r^2)^(3/2) i think

Answer 3

but i need help with the bounds

Answer 4

The bounds would be, theta would be 0 to 2 pi. The radius, r, would be from a to b, then phi would be from 0 to pi. That is the write conversion to spherical.

Answer 5

So your integral would look like this:
\[\int\limits_{0}^{2 \pi} \int\limits_{0}^{\pi} \int\limits_{a}^{b} \frac{\rho^2 \sin(\phi)}{(\rho^2)^{3/2}}d \rho d \phi d \theta\]

Answer 6

how come u used rho instead of r?

Answer 7

r typically is used in polar/cylindrical to show the radius of a circle. Rho is typically used in spherical to denote the radius of a sphere.

Answer 8

oh duh i forgot i was doing spherical coordinates for a second. thanks for the help :)

Answer 9

so in spherical coordinates is dV=rho^2 sin(phi)?

Answer 10

Yessir.

Answer 11

cooool just making sure