vault backup: 2025-03-27 09:46:27

This commit is contained in:
arc 2025-03-27 09:46:27 -06:00
parent 3ce3b8a446
commit d78c1ecd7a
2 changed files with 6 additions and 27 deletions

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@ -1,27 +0,0 @@
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@ -86,3 +86,9 @@ Average = $\dfrac{1}{b-a} \int_a^b f(x)dx$
# The Fundamental Theorem of Calculus
Let $f$ be a continuous function on the closed interval $[a, b]$ and let $F$ be any antiderivative of $f$, then:
$$\int_a^b f(x) dx = F(b) - F(a)$$
## Proof
## Mean Value Theorem
Between the interval $[a, b]$, the average rate of change of a function **must be equal** to at least one point between $[a, b]$:
$$ f'(c) = \dfrac{f(b) - f(a)}{x-a} $$
For some $c$ between $a$ and $b$.