Evaluate the line integral ,
where C is the line segment from (0,4,7) to (2,8,6).

150.134

The work

2.

Evaluate the line integral ,
where C is the right half of the circle .

31250

The work

3.

Compute the total mass of a wire bent in a quarter circle with parametric
equations: x = 5cos(t), y = 5sin(t), 0 &le t &le &pi/2 and
density function .

196.35

The work

4.

Let C be the curve which is the union of two line segments, the first going from
(0, 0) to (-1, -4) and the second going from (-1, -4) to (-2, 0).
Compute the line integral .

-8

The work

5.

Let F be the radial force field F = xi + yj. Find
the work done by this force along the following two curves, both which go from
(0, 0) to (4, 16).

A. If is the parabola: ,
then

B. If is the straight line segment: , then

A) 136
B) 136

The work

6.

Evaluate the line integral , where
F(x, y, z) = 4xi - 5yj - zk and C
is given by the vector function r(t) = &lang sin(t), cos(t), t &rang, 0 &le t &le 3&pi/2.

-6.6033

The work

7.

Evaluate the line integral , where
F(x, y, z) = (5sinx)i - (4cosy)j + xzk and C
is given by the vector function
, 0 &le t &le 1.

5.864

The work

8.

Find the work done by the force field
F(x, y, z) = 1xi + 1yj + 7k on a particle that moves along the helix .