Question

Find work done by F= along the polygonal path from (0,-1,1) to (2,0,1) to (2,2,2), to (0,2,5), to (pi,3,2). I believe Fundamental Theorem for Line Integrals is needed. is (0,-1,1) the initial and (pi,3,2) the final point? so the rest of the points are unnecessary?

Answer 1

Yes, Fundamental Theorem of Line Integrals

\[\int_c \nabla f \bullet dr= f(r(b))-f(r(a))\]
where [a,b] are the beginning and ending points of the path parametrized by r(t). So, you can ignore all the points in between....plus, from physics we know that work is independent of path so only initial and final position are important.

Answer 2

THANK YOU. that's all the help i needed. I shall post my answer later to double check.

Answer 3

My work:
First, I integrate F to f(x,y,z) and got xyz+y^2z+sinx.
Then I plugged in w= f(pi,3,2) - f(0,-1,1) and got 6pi+17.
How does that answer sound?