Aparticle moves along line segments from the origin to the points (2, 0, 0), (2, 4, 1), (0, 4, 1), and back to the origin under the influence of the force field. f(x, y, z) = z^2i + 3xyj + 2y^2k. find the work done.

The work is equal to the line integral of over each line segment.

Parameterize the paths

The work done by over each segment (call them ) is

Then the total work done by over the particle's path is 46.

3< x< 5

step-by-step explanation:

|x - 4| < 1

there are two solutions, one positive and one negative.   remember to flip the inequality when taking the negative solution

x-4 < 1       x-4 > -1

add 4 to each side

x-4+4 < 1+4       x-4+4 > -1+4

x< 5                 x> 3

3< x< 5

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