
Stokes' Theorem
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:
[(32)(0)+(x)] = 1x
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) + (0x) = 1  x
So, i'm not sure whether the correct answer for that part is
(1x) or (1x)
I'm thinking that (1x) is correct because it is oriented counterclockwise.
So, if that is the case i get:
integral integral (1x)dA
= integral(0, 2pi) integral(0, 3) (1rcos(theta))r dr d(theta)
Did i do this correctly?