Question

Find the work done by the force F(x, y) = 2xyi + 4y2j acting along the piecewise smooth curve consisting of the line segments from (-2,2) to (0,0) and from (0,0) to (2,3).

Answer 1

The first line is parametrized by
x(t)=t and y(t)=-t ,
\[ -2 \le t \le 0\]
Compute F(x(t),y(t)) . ( x'(t), y'(t)) and integrate
from t=-2 to t=0.
Mimic for the second line.

Answer 2

F(x(t),y(t)) . ( x'(t), y'(t))
This is the dot product