Chapter 6.8, Problem 1P

Evaluate the line integral ${\displaystyle \int \left(x^2-y^2\right)}dx-2xydy$ along each of the following paths from $(0,0)$ to $(1,2)$.

(a) $y=2x^2$.

(b) $x=t^2,y=2t$.

(c) $y=0$ from $x=0$ to $x=2;$ then along the straight line joining $(2,0)$ to $(1,2)$.