How is the Net Change Theorem different from Fundamental Theorem Of Calculus II
Matthew Barrera 
1) Fundamental Theorem Of Calculus II $$ \int_{a}^{b}f'(x) = f(b) - f(a)$$ 2) Net Change Theorem $$ \int_{a}^{b}f'(x) = f(b) - f(a)$$
They are the same, why have two?
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$\begingroup$They are the same, but "net change theorem" is arguably a better/more descriptive name.
(I like this name because it emphasizes the intuition that we are adding up a bunch of tiny or "infinitesimal" changes to obtain the net change. I think many calculus classes fail to convey this intuition.)
$\endgroup$ 1 $\begingroup$Context matters. Mathematically they are the same but people may use them when referring to differing things. For example the net change theorem may be better written as: $$\int_a^br(t)dt=Q(b)-Q(a)$$ When discussing it like this r(t) is specifically the rate of flow for some "charge" Q. And the net charge is $\Delta Q= Q(b)- Q(a)$
A similar more physical example of this is the concept of voltage and electro-motor force. Both are the same thing but different groups solving different problems came to the same conclusion more or less independently and as a result we have two conventions that have not unified.
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