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[spec] length of a curve
author
Andrew Lorimer
<andrew@lorimer.id.au>
Mon, 13 May 2019 06:49:26 +0000
(16:49 +1000)
committer
Andrew Lorimer
<andrew@lorimer.id.au>
Mon, 13 May 2019 06:49:26 +0000
(16:49 +1000)
spec/calculus.md
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spec/calculus.md
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spec/calculus.md
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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