Evaluating line and surface integrals...?

Question

1.) Evaluate the field F=(x+yz)i+ (y+xz)j+(z+xy)k alond the straight line from (1,0,0) to (1,1,0) and then from (1,1,0) to (1,1,1).

2,) Evaluate the surface integral...
v=(y^2)i + (2xy+z^2)j+(2yz)k S; the unit cube centered at the origin.

3.) Evaluate the surface integral...
v=(2xz+3y^2) j + (4yz^2) k , S: the square in the yz-plane having corners (0,0,0), (0,1,0), (0,1,1), and (0,0,1).

Answer 1

1)If you Take the scalar function
H = 1/2( x^2+y^2+z^2) +xyz
Hx= x+yz
Hy= y+xz
Hz= z+xy
H is the potential function of the field and the integral does not depend on the way
First integral = 1/2(1+1) - 1/2(1) = 1/2
The second = 3/2+1 -(1) = 3/2