- #1
sunnyday11
- 14
- 0
Homework Statement
Verify Stoke's Theorem for F = y i + z j + x k and S the paraboloid z=1-(x^2+y^2) with z bigger or equal to 0 oriented upward, and the curve C which is the boundary of S.
Homework Equations
Stoke's Theorem
line interal = flux of curl of F (don't know how to use the symbol function)
The Attempt at a Solution
For the line integral, I use r(t) = cos (t) i + sin (t) j , and the solution i got was -pi but I could not get the flux of curl of F to match.
Curl F = -(i+j+k)
double integral of (-2x-2y-1)dxdy
==> double integral of (-2r cost(t) - 2r sin(t) drdt with r [0,1] and t [0, 2pi]
Thank you very much!