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## Homework Statement

Trying to derive the work-energy theorem, without manipulating differentials.

## Homework Equations

a=[itex]\frac{dv}{dt}[/itex] v=[itex]\frac{dx}{dt}[/itex]

W=[itex]\int[/itex] F dx =ΔKE=[itex]\frac{1}{2}[/itex]mvf[itex]^{2}[/itex]-mvi[itex]^{2}[/itex]

## The Attempt at a Solution

F=ma

[itex]\int[/itex] F dx=m[itex]\int[/itex]a dx

=m[itex]\int[/itex][itex]\frac{dv}{dt}[/itex]dx <-- I cannot continue, unless I start using the differentials as fractions. Can you move forward without thinking of them as fractions? Or if you choose to use them as fractions could you justify the act?

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