R is the region enclosed by a sphere of radius 5 and the plane z=3.
Write an integral in spherical coordinates representing the volume of this region and evaluate it. (Would be much easier in cylindrical, but that is the problem before this one)
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Here's what I tried but it just doesn't seem right:
3/(cos(phi)) <= rho <= 5
0 <= phi <= cos^-1(3/5)
0 <= theta <= 2*pi
using I to represent the integral and the boundaries of integration as above,
III(rho^2)*sin(phi) d-rho d-phi d-theta
This is impossible to integrate and doesn't come out with a reasonable value plugged into my calculator, so I know I'm doing something wrong or overcomplicating this. Please help!
Write an integral in spherical coordinates representing the volume of this region and evaluate it. (Would be much easier in cylindrical, but that is the problem before this one)
------
Here's what I tried but it just doesn't seem right:
3/(cos(phi)) <= rho <= 5
0 <= phi <= cos^-1(3/5)
0 <= theta <= 2*pi
using I to represent the integral and the boundaries of integration as above,
III(rho^2)*sin(phi) d-rho d-phi d-theta
This is impossible to integrate and doesn't come out with a reasonable value plugged into my calculator, so I know I'm doing something wrong or overcomplicating this. Please help!