- #1
pcjang
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Homework Statement
I was studying for my finals, and then the only thing that I got stuck on was parameterizing a surface and finding the area of the surface.
and my problem states that x2 + y2 + z2 = 4
and z [tex]\geq[/tex][tex]\sqrt{2}[/tex]
Homework Equations
so when parameterizing a sphere, it comes out to be
x = r sin[tex]\phi[/tex]cos[tex]\theta[/tex]
y = r sin[tex]\phi[/tex]sin[tex]\theta[/tex]
z = r cos[tex]\phi[/tex]
The Attempt at a Solution
so I'm sure that [tex]\theta[/tex] goes from 0 to 2[tex]\pi[/tex]. But i was getting confused what boundaries should be for [tex]\phi[/tex].
What i tried is that
since z [tex]\geq[/tex][tex]\sqrt{2}[/tex] and should be less than 2 since 2 is the radius, i put [tex]\sqrt{2}[/tex] [tex]\leq[/tex] z [tex]\leq[/tex] 2.
which z = 2 cos[tex]\phi[/tex]
so when i solved it, it came out to be [tex]\pi[/tex]/4 [tex]\leq[/tex] [tex]\phi[/tex] [tex] leq[/tex] 0.
but it just doesn't make sense to me how the boundary can go backwards. can someone explain to me~??