- #1
Wildcat04
- 34
- 0
Homework Statement
Evaluate: [tex]\int[/tex][tex]\int[/tex]G(r)dA
Where G = z
S: x2 + y2 + z2 = 9 [tex]z \geq 0[/tex]
Homework Equations
Parameterization
x = r sinu cosv
y = r sinu sin v
z = r cos u
The Attempt at a Solution
r(u,v) = (r sinu cosv)i + (r sinu sinv)j + (r cosu)k
ru = (r cosu cosv)i + (-r cos u sinv)j + (-r sinu)k
rv = (-r sinu sinv)i + (r sinu cosv)j + 0k
dA = |ru x rv|
I am not sure if I am approaching this correctly or if I am way off base. My next step was to complete the dot product of z with dA but this does not seem right and I can't find any good examples in my text.
Thank you in advance.