Here's how roughly: Define K(x) as [itex]K(x) = \frac{1}{2}mv(x)^2[/itex]. Define [itex]W_{a \rightarrow b}[/itex] as [itex]\int_a^b F(x')dx'[/itex]. Show that [itex]W_{a \rightarrow b} = K(b) - K(a)[/itex]. Then define U(x) as [itex] -\int_s^x F(x')dx'[/itex] where s is a fixed arbitrary point, and show that [itex]U(b) - U(a) = -W_{a \rightarrow b} [/itex]. Then define the energy E of the system as E(x) = K(x) + U(x). Show how the previously found result imply that E is a constant.
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