Use Stokes' Theorem to evaluate

integral(c) F * dr

C is oriented counterclockwise as viewed from above.

F(x,y,z)= xyi + 2zj + 3yk

C is the curve of intersection of the plane x + z = 5 and the cylinder x^2 + y^2 = 9

Stokes theorem:

integral integral [-(dR/dy - dQ/dz)dz/dx - (dP/dz - dR/dx)dz/dy + (dQ/dx - dP/dy)] dA

When i used this i got:

[-(3-2)-(0)+(-x)] = -1-x

I tried this another way and got:

(3y d/dy - 2z d/dz) - (3y d/dx - xy d/dz) + (2z d/dx - xy d/dy)

= (3 - 2) - (0) + (0-x) = 1 - x

So, i'm not sure whether the correct answer for that part is

(-1-x) or (1-x)

I'm thinking that (1-x) is correct because it is oriented counterclockwise.

So, if that is the case i get:

integral integral (1-x)dA

= integral(0, 2pi) integral(0, 3) (1-rcos(theta))r dr d(theta)

Did i do this correctly?