The force field F(x, y) = (x + y)i + (x + 1)j acts on an object moving from the point (0, 0) to the

The force field F(x, y) = (x + y)i + (x² + 1)j acts on an object moving from the point (0, 0) to the point (0, 1), as shown in the figure.

(a) Find the work done when the object moves along the path x = 0, 0 ≤ y ≤ 1.

(b) Find the work done when the object moves along the path x = y - y²,0 ≤ y ≤ 1.

(c) The object moves along the path x = c(y - y²), 0 ≤ y ≤ 1,
c > 0. Find the value of the constant c that minimizes the
work.

y 1 X