Verification Of Stoke's Theorem

[Baumer8993]

Homework Statement

Verify Stoke's Theorem by computing both integrals: (stoke's theorem, and the original work integral).
σ is the portion of z = sqrt(4-x²-y²) above the xy-plane and the vector field is F = <2x-y, y*z², y²z>

Homework Equations

stoke's theorem, and work integral

The Attempt at a Solution

When I do stoke's theorem I get <0,0,1> for my curl F. My normal vector is <2x, 2y, 2z>. After I do the two, and do the integral I get 33.51 for my answer.

My work integral I have <2cos(t), 2sin(t)> for my parametrization path. However, when I do the integral I get 12.5. I am not sure which one is right since I have tried the problem three times, but I always get the same answer, so I do not know what to do.

 

[LCKurtz]

Homework Statement

Verify Stoke's Theorem by computing both integrals: (stoke's theorem, and the original work integral).
σ is the portion of z = sqrt(4-x²-y²) above the xy-plane and the vector field is F = <2x-y, y*z², y²z>

Homework Equations

stoke's theorem, and work integral

The Attempt at a Solution

When I do stoke's theorem I get <0,0,1> for my curl F. My normal vector is <2x, 2y, 2z>. After I do the two, and do the integral I get 33.51 for my answer.

My work integral I have <2cos(t), 2sin(t)> for my parametrization path. However, when I do the integral I get 12.5. I am not sure which one is right since I have tried the problem three times, but I always get the same answer, so I do not know what to do.

Do you expect us to work both sides out to see what we get? Show us what you did and we can likely quickly find your mistake.