Integrating Force: Understanding \oint and \int

Thread starter UrbanXrisis
Start date Dec 18, 2004
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Force Integrating

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The discussion centers on the relationship between force integration and potential energy, specifically addressing whether the integral of force equals negative potential energy, expressed as ∫F = -U. Participants clarify that the equation F = -dU/dx supports this relationship. The difference between the integral symbols ∮ and ∫ is also explained, with ∮ representing a closed loop integral, while ∫ denotes a standard integral over a range. Additionally, it is noted that the closed integral can apply to both closed and open curves. Understanding these concepts is crucial for analyzing work and energy in physics.

Dec 18, 2004

UrbanXrisis

does the integration of Force equal negative potential energy?

\int{F}={-U}

Also, what is the difference between \oint and \int?

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Dec 18, 2004

Nylex

Yeah, it should seeing as F = - dU/dx.

The integral sign with a circle is an integral around a closed loop/surface I think, whereas the normal integral sign isn't.

Dec 18, 2004

UrbanXrisis

so: W’=F=-dPE/dt

Dec 18, 2004

arildno

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The \oint is often used for a curve integral (whether or not the curve is looped (closed) or not).

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