1. Compute
along the quarter circle from (1,0) to (0,1).
1. Compute
along the quarter circle from (1,0) to (0,1).
2. Evaluate 
where C is the line segment from (1,0) to (2,
).
3. Evaluate 
, where F(x,y,z) = 4xi - 3yj + 7zk and S is the
surface of the cube bounded by the coordinate planes and the planes x=1, y=1,
and z=1.
4. Evaluate 
, where F(x,y,z) = xi + yj + 2zk and S is the
portion of the cone z2 = x2 + y2 between
the planes z = 1 and z = 2, oriented upwards.
5. Evaluate 
, where C is the circle x2 + y2 = 4 with counterclockwise
orientation..
6. Evaluate 
, where S is the surface of the solid bounded by z=4-x2, y+z=5,
z=0, and y=0.
7. Compute 
where F(x,y,z) = yi + zj - xk and C is the line
segment from (1,1,1) to (-3,2,0).
8. Compute 
where C is the triangle with vertices (0,0), (2,0), and (0,4).
9. Evaluate 
10. Compute 
, where F(x,y,z) = 2yj + k and S is the portion of the
paraboloid z = x2 + y2 below the plane z = 4 with positive
orientation.