## Line Integrals and Stokes' Theorem

Hello guys, I'm sorry for taking advantage of you but I need your help. I understand Stroke Theorem but I getting stuck on the following problems:

1. Let C be the intersection curve of the surfaces z =3x-7 and
x2 + y2 = 1, oriented clockwise as seen from above.
Let F = (4z-1)i + 2xj + (5y + 1)k. Compute the work integral ∫F dr, in two ways:
(a) directly as a line integral
(b) as a double integral, using Stokes' Theorem.

2. Let S be the surface described by z = x2 + y2 ; z ≤ 4 ; y 0 and let C be the boundary curve of S with the orientation clockwise.
Let F= < y, z, x >. Find ∫F dr, in two ways:
(a) directly as a line integral
(b) as a double integral, using Stokes' Theorem.

3. Let S be the part of the surface z = 1-x2 in the first octant with 0 ≤ y ≤ 2. Let C be the boundary of S, oriented counterclockwise when viewed from above. Let F = <1, 0, y2 >. Calculate ∫F dr in two ways:
(a) directly as a line integral
(b) as a double integral, using Stokes' Theorem.