From b23a4190d4418721123fcc9c7d0c9408a8df32dc Mon Sep 17 00:00:00 2001 From: Andrew Lorimer Date: Mon, 6 May 2019 17:22:21 +1000 Subject: [PATCH] [spec] fundamental theorem of calculus --- spec/calculus.md | 8 ++++++++ 1 file changed, 8 insertions(+) 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 $f$ -- 2.43.2