From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Mon, 6 May 2019 07:22:21 +0000 (+1000)
Subject: [spec] fundamental theorem of calculus
X-Git-Tag: yr12~149
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/b23a4190d4418721123fcc9c7d0c9408a8df32dc?ds=sidebyside;hp=d4a675635856335fa2c4d674c72c645ba2fd5b6f

[spec] fundamental theorem of calculus
---

diff --git a/spec/calculus.md b/spec/calculus.md
index 671f0fa..b454072 100644
--- a/spec/calculus.md
+++ b/spec/calculus.md
@@ -326,3 +326,11 @@ $$f(x) = {P(x) \over Q(x)} \quad \text{where } P, Q \text{ are polynomial functi
 - when two graphs have the same ordinate, $y$-coordinate is double the ordinate
 - when two graphs have opposite ordinates, $y$-coordinate is 0 i.e. ($x$-intercept)
 - when one of the ordinates is 0, the resulting ordinate is equal to the other ordinate
+
+## Fundamental theorem of calculus
+
+If $f$ is continuous on $[a, b]$, then
+
+$$\int^b_a f(x) \> dx = F(b) - F(a)$$
+
+where $F$ is any antiderivative of $f$