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- Thread starter Periapsis
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- #2

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Differentiation and integration have uses FAR beyond those simple geometric interpretations.

- #3

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$$ \int_a^b f(x) = F(b) - F(a)$$

A basic example in physics with real-world application that beautifully illustrates this relationship and shows a need for integration is as follows: An object tracks it's position and records it's total distance traveled at a given time to function d(t). By differentiating this with respect to t, you get it's velocity at any given time v(t)=d'(t). Now, say for some reason you only know the velocity function and need to get distance traveled between two times. You simply Integrate v(t) between those 2 points with respect to t and you have the change in distance.

- #4

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Thank you very much! I'll have to read into that Theorem

- #5

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You're welcome! Glad I could help :)

- #6

HallsofIvy

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arildno

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We would then have added up all the tiny bits of stuff whenever we needed to do that.

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