I'm doing some problems in James Stewart's Calculus Concepts and Contexts (2nd ed.), and stumbled upon question 37 in section 13.2: Line Integrals, and it is giving me a bit of trouble. Here is a link to a screenshot of the problem: https://i.stack.imgur.com/O8ZoF.png.
My interpretation: We can estimate the work done, in joules, as the sum of the dot products between all the unit tangents and their respective force vectors provided by the diagram. This works because we only care about how much force these vectors act in the direction of the object that's moving.
So at quick glance, we have 2+2+2+2+1+1+1=11, but the answer book says that the answer is 22. I am a bit confused where this constant of 2 is coming from. Thanks for the help!
$W = \Sigma F \cdot s$, or work = force $\times$ distance.
The distance moved by the object in each step is $2$, so you have $11 \times 2 = 22$.
Note to readers: the force in the direction of motion, not the total force.