So the question says:
Find the work done by the force field F = (2x+y-yz, x+y-xz, -xy-3z^2)
on a particle moved along the straight line from (0,2,1) to (1,4,0)
Soooo what I've done is:
the straight line is parametrized by:
x = 0.5 t
y = t + 2
z = -0.5 t + 1
Then F = (t+t+2 - (t+2)(-0.5t+1), 0.5t +t+2-0.5t(-0.5t+1), -0.5t(t+2)-3(-0.5t+1)^2)
So then F = (0.5t^2+2t, 0.25t^2+t+2, -1.25t^2+2t-3).
Therefore work = integral(0 to 2) of F dot ds
= integral(0 to 2) of (0.5t^2+2t, 0.25t^2+t+2, -1.25t^2+2t-3) dot (0.5t, t+2, -0.5t+1)
which works out to be 127/6
Is this correct? I'm not at all sure about the parametrization, is there an easier way of doing this???
Thanks in advance for any help!