"the x component of the force on an object varies as shown in fig. 6-36.
figure 6-36
(a) determine the work done by this force to move the object from x = 0.0 to x = 3.0 m.
j
(b) determine the work done by this force to move the object from x = 0.0 to x = 10.0 m.
j"

a) 2,800Joules

b)600 Joules

Explanation:

a) we're basically looking at a force x position graph. And we may know already that work = the force x the  displacement, but since this only works if the force is constant (when this happens it looks like a straight line making a square/rectangular graph with respect to position in m) So, in order to do this with varying force, you take the area of the inside shape made by the graph! This is going to give you the value for the work done. From x=0 to x= 10 it looks we have a nice old traoezoid. The area of a trapezoid is A=(a+b)/2 *h. a being the top of the trapezoid, b being the base of the trapezoid, and h being the height of the trapezoid.

A= (4 +10)/2 *400

A= 2,800 Joules

b) same thing, find the area. This time its a triangle so the Area= 1/2 b*h

So, it ends up being 1/2(3*400)

A=600 Joules