From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Tue, 9 Apr 2019 06:08:16 +0000 (+1000)
Subject: Merge branch 'master' of ssh://charles/tank/andrew/school/notes
X-Git-Tag: yr12~168
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/9b4ce53d414fedba7ccafc9534dee37f57d74372

Merge branch 'master' of ssh://charles/tank/andrew/school/notes
---

9b4ce53d414fedba7ccafc9534dee37f57d74372
diff --cc spec/calculus.md
index 5be3218,167a7e7..ddda405
--- a/spec/calculus.md
+++ b/spec/calculus.md
@@@ -248,7 -247,13 +258,11 @@@ $\int k f(x) dx = k \int f(x) dx
  | ${f^\prime (x)} \over {f(x)}$ | $\log_e f(x) + c$ |
  | $g^\prime(x)\cdot f^\prime(g(x)$ | $f(g(x))$ (chain rule)|
  | $f(x) \cdot g(x)$ | $\int [f^\prime(x) \cdot g(x)] dx + \int [g^\prime(x) f(x)] dx$ |
 -| ${1 \over {ax+b}}$ | ${1 \over a} \log_e (ax+b) + c$ |
 -| $(ax+b)^n$ | ${1 \over {a(n+1)}}(ax+b)^{n-1} + c$ |
  
+ ### Definite integrals
+ 
+ $$\int_a^b f(x) \cdot dx = [F(x)]_a^b=F(b)-F(a)_{}$$
+ 
  ## Applications of antidifferentiation
  
  - $x$-intercepts of $y=f(x)$ identify $x$-coordinates of stationary points on $y=F(x)$