Because force[x] changes very little between each plotted point on the x-axis, the work done by the force in moving from a plotted point {x, 0} to the next plotted point {x + jump, 0} is well approximated by force[x] jump. This is the same as the area of a box whose left side touches the x-axis at {x, 0}. As a result, the accumulated work in moving all the way from x = 0 to x = 6 is well approximated by Sum[force[x] jump,{x, 0, 6 - jump, jump}]. Use this as a start to try to explain why physicists say that the work done by the force field as the object moves from x = 0 to x = 6 is Integrate[force[x], {x, 0, 6}]

Sticking with the same force[x] as above, look at some boxes n21] Clear[jump, points, box, boxes, x, n]; Jump[n_1 (b - a); points[n] Table[Graphics[ (PointSize[e.01], Red, Pointlfx, e)]], (x, a, b - jump[n], jump[n]] box[n-, x_1 := Graphics [ Line[{{x, e), {x, force[x]), {x + Jump[n], force(x]), {x + Jump[n], ), {x, boxes[n_] := Table[box[n, x], {x, a, b - Jump[n], Jump[n]}); BoxStory[n ] Show[forceplot, boxes[n], points[n], AspectRatio -Automatic]; Show[ BoxStory[5e]] e}}]]; Du29 0.5 -0.5 Because force[x] changes very little between each plotted point on the x-axis, the work done by the force in moving from a plotted point (x, 03 to the next plotted point (x +jump, 03 is well approximated by force[x] jump This is the same as the area of a box whose left side touches the x-axis at x. 0j As a result, the accumulated work in moving all the way from x = 0 to x = 6 is well approximated by Sum forcelx]ump,x, 0ump, jump] Use this as a start to try to explain why physicists say that the work done by the force field as the object moves from x-0 tox 6 is force x] dx In[30] Integrate[force[x], (x, e, 6)] 3.07807