Hello,
The bound for y will be 0 and 2 :
0<y²<4-x²-z²<4
y>0
-> y<sqrt(4)=2
0<y<2
Are there any information about x or z ?
I am confused on how the bounds on the question are found. Here's the question.
Use spherical coordinates to find the mass of the solid enclosed by the hemispherical region and with a density function (x,y,z)=
also, the < signs are suppose to be "less than or equal to"
Looks to me like the hemisphere is the right half of a sphere centred on the origin.
You're told to work in spherical coordinates, right? So:
Radius: .
Azimuthal angle in the xy-plane: .
Polar angle from the z-axis: .
Of interest: Spherical Coordinates
Yep that's it. Is theta 0 to Pi because its half a sphere? Also, why is the phi 0 to Pi also, I can't really picture it.
EDIT: Ok, I can see why its Pi now, I am confused from the question. I can't really see what [tex] x^2+y^2+z^2<4 [/tex] and is. What do these regions mean?