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education/math/MATH1210 (calc 1)/Integrals.md

@@ -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 $b$.