My Thermodynamics teacher used the relation in the image and I would like to know how can I prove it!
https://i.stack.imgur.com/EQlB4.jpg
Thank you!
2026-03-30 20:42:51.1774903371
Expressing Δf with an integral of a differential (infinitesimal)
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This is just the fundamental theorem of calculus. If $\Delta x$ is a finite distance on the $x$-axis, then the corresponding change in $f$ is simply $$\Delta f = f(x + \Delta x) - f(x) = \int_x^{x + \Delta x} f'(x)\, dx.$$