vault backup: 2025-04-06 12:18:45

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arc 2025-04-06 12:18:45 -06:00
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@ -88,6 +88,7 @@ Average = $\dfrac{1}{b-a} \int_a^b f(x)dx$
$$\int_a^b f(x) dx = F(b) - F(a)$$
2. Let $f$ be a continuous function on $[a, b]$ and let $x$ be a point in $[a, b]$.
$$ F(x) = \int_a^x f(t)dt \Rightarrow F'(x) = f(x) $$
This basically says that cancelling out the derivative from $a$ to $x$ can be done by
$$ \dfrac{d}{dx} \int_a^{g(x)} f(t) dt = f(g(x)) * g'(x)* $$
## Examples
> Finding the derivative of an integral