Posted in Health-01-01 by admin
on June 30, 2006
Advanced Triple
Setting up the triple integral in spherical coordinates to find the volume of a solid? Help!?
The question reads: Consider the solid region D between the spheres x^2+y^2+z^2=1 & x^2+y^2+z^2=9 and above the upper nappe of the cone z^2=3(x^2+y^2). How would you describe to solid region in spherical coordinates? And how would you set up the triple integral in spherical coordinates that can be used to find the volume V of this solid. Any help would be greatly appreciated. Thanks in advance.
The following describes the region in spherical coordinates:
The angle with respect to the z-axis, (I think it is phi, but I might have it mixed up with theta) goes from 0 to pi/6
The radius, rho, goes from 1 to 3.
The angle with respect to the x-axis (I think theta) goes from 0 to 2pi
Set up the triple integral with the limits above and you are integrating
rho^2 (sin phi) d theta d phi
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