From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Mon, 13 May 2019 06:49:26 +0000 (+1000)
Subject: [spec] length of a curve
X-Git-Tag: yr12~140
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/025be5af98c3da2da0a784bed2b68b45ce3021c7

[spec] length of a curve
---

diff --git a/spec/calculus.md b/spec/calculus.md
index 63b2e90..9d9ed36 100644
--- a/spec/calculus.md
+++ b/spec/calculus.md
@@ -345,6 +345,16 @@ Approximate as sum of infinitesimally-thick cylinders
 $$V = \pi \int^b_a f(x)^2 - g(x)^2 \> dx$$  
 where $f(x) > g(x)$
 
+## Length of a curve
+
+$$L = \int^b_a \sqrt{1 + ({dy \over dx})^2} \> dx$$
+
+Evaluate on CAS. Or use Interactive $\rightarrow$ Calculation $\rightarrow$ Line $\rightarrow$ `arcLen`.
+
+### Parametric curve
+
+$$l = \int^b_a \sqrt{({dx \over dt})^2 + ({dy \over dt})^2} \> dt$$
+
 ## Rates
 
 ### Related rates