Question 8

A particle moves in the plane from $A = [1, -2]$ to $B = [4, 4]$ along the straight line segment $AB$.
The particle is acted on by two forces, $\underline{G}$ and $\underline{H}$ at any point $[x, y]$ of the segment:

$$\underline{G} = [3, 5] ,$$

$$\underline{H} = [\sqrt{x}, 3y^2].$$

Calculate the work done by each of the forces as the particle moves from $A$ to $B$.