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I've gone through all of the archives and read through the threads that seem to be about what I am learning in this course, F=ma, and the W.E.T. and Conserv. of Energy, and Conserv. of Momentum. So far, I haven't really found many threads that seem to have any relevance to what I am trying to learn. Our comprehensive final is worth 40% of our GPR so I plan on making this site my new home for the new 5 weeks or so for sure.

Now, after that great narrative, here is my conundrum (trying to sounds like a smart kid). The exam I will be taking this Wednesday will be mainly over Kinematics, Work-Energy Theorem, Conservation of Energy, and Conservation of Momentum. We don't get to any circular motion until after this exam. I am having a lot of trouble understand the line integral when defining the Work of the Forces on a particle. I have no idea how to put the equations in this post, so I will explain in as much detail as possible.

This is the equation I am having a difficult time grasping:

W(of the force, from r_1, to r_2) = the Integral(from r_1, to r_2) of the vect.Force * d(vect r)

I've seen in other threads that the "d*r" in that equation can be listed in several different ways, but this is the way it is in my text.

Is there any way someone could explain how this line integral is giving the total work?

I understand the KE and PE equations, where I just insert the knowns and solve for the unknowns.

I don't understand how taking the anti-derivative of a Force and then multiplying it by the distance the Force "went" is going to give me how many joules of Energy.

I apologize for such a long post, and if the answer is somewhere else, and I have missed it, just direct me to the correct place and no answer will be needed.

Thank you for your time.

-B.G.