From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Mon, 6 May 2019 12:03:33 +0000 (+1000)
Subject: [spec] properties of definite integrals
X-Git-Tag: yr12~148
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/c852a21dec0421aece1c2b4b9845e9d56d3573bb

[spec] properties of definite integrals
---

diff --git a/spec/calculus.md b/spec/calculus.md
index b454072..b89eae6 100644
--- a/spec/calculus.md
+++ b/spec/calculus.md
@@ -254,6 +254,18 @@ $$\int_a^b f(x) \cdot dx = [F(x)]_a^b=F(b)-F(a)$$
 - *Integrand* is $f$.
 - $F(x)$ may be any integral, i.e. $c$ is inconsequential
 
+#### Properties
+
+$$\int^b_a f(x) \> dx = \int^c_a f(x) \> dx + \int^b_c f(x) \> dx$$
+
+$$\int^a_a f(x) \> dx = 0$$
+
+$$\int^b_a k \cdot f(x) \> dx = k \int^b_a f(x) \> dx$$
+
+$$\int^b_a f(x) \pm g(x) \> dx = \int^b_a f(x) \> dx \pm \int^b_a g(x) \> dx$$
+
+$$\int^b_a f(x) \> dx = - \int^a_b f(x) \> dx$$
+
 ### Integration by substitution
 
 $$\int f(u) {du \over dx} \cdot dx = \int f(u) \cdot du$$
@@ -292,7 +304,7 @@ Use identities:
 - $\cos^2x={1 \over 2}(1+\cos 2x)$
 - $\sin 2x = 2 \sin x \cos x$
 
-### Partial fractions
+## Partial fractions
 
 On CAS: Action $\rightarrow$ Transformation $\rightarrow$ `expand/combine`