vault backup: 2025-08-25 12:19:25

education/math/MATH1220 (calc II)/Integral Review.md

@@ -0,0 +1,12 @@
+# Formal Definition
+Let $f$ be a continuous function on an interval $[a, b]$.
+
+Divide $[a, b]$ into $n$ equal parts of width $\Delta x = \dfrac{b-a}{n}$.
+
+Let $x_0, x_1, x_2, \cdots, x_n$ be the endpoints of this subdivision. $x_0 = a$ and $x_n = b$. 
+
+Define $$\int_a^b f(x) dx = \lim_{n \to \infty} \sum_{i=1}^nf(x_i)\Delta x$$
+- $\Delta x$ refers to the width of each sub-interval
+- $f(x_i)$ refers to the height of each subinterval.
+
+Then let $f$ be a continous function on $[a, b]$ and let $F$ be the any derivative of $f$ (i.e )