How to do the given Line Integral problem in Maple ? Find the work done by the force F along C.

Question

How to do the given Line Integral problem in Maple ? Find the work done by the force F along C. F(x, y, z) = (y, −x, −z), C consists of the line segments from (0, 1, 0) to (3, 2, −1), (3, 2, −1) to (−1, 4, 2), (−1, 4, 2) to (2, −1, 4), and (2, −1, 4) to (0, −2, −2).

I did the following by hand and got the answer but I have no idea to do it in maple W = -X -2X +5X + X + 3Y -4Y +3Y -2Y +Z -3Z -2Z + 6Z W = 3X + 0 + 2Z W = 3X + 2Z

Answer 1

Since you mentioned Maple,

restart;
with(VectorCalculus):

SetCoordinates('cartesian'[x,y,z]):

pts := <0,1,0>, <3,2,-1>, <-1,4,2>,
       <2,-1,4>, <0,-2,-2>:

LineInt(VectorField(<y,-x,-z>), LineSegments(pts), inert):

     Int(3-t,t = 0 .. 1) + Int(-11-9*t,t = 0 .. 1)
   + Int(3-4*t,t = 0 .. 1) + Int(28-36*t,t = 0 .. 1)

value(%);

                  -2

# Perhaps you tried something like this (by hand)?

LineInt(VectorField(<Y,-X,-Z>), LineSegments(pts), inert):

     Int(3*Y-X+Z,t = 0 .. 1) + Int(-4*Y-2*X-3*Z,t = 0 .. 1)
   + Int(3*Y+5*X-2*Z,t = 0 .. 1) + Int(-2*Y+X+6*Z,t = 0 .. 1)

value(%);

                3 X + 2 Z