- #1
sunnyday11
- 14
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Homework Statement
F = ( 2y i + 3x J + z2 k where S is the upper half of the sphere x2 + y2 + z2 = 9 and C is its boundary.
Homework Equations
The Attempt at a Solution
I used Stoke's Theorem and found the solution to be 36 pi, but when I use line integral to verify, using substition:
r(t) = 3cost i + 3sin t j
F(r(t))r'(t) = 9 (-2sin2t + 3cos2t)
[tex]\int^{2 pi}_{0}[/tex] 9 (-2sin2t + 3cos2t)
= 9 (1/2 + 5/2 cos(2t))[tex]/^{2 pi}_{0}[/tex]
= 9 pi which doesn't agree with 36 pi.
I wonder if I did my substitution wrong. Should I do anything with z or the k component?
Thank you!