Recall how to calculate the arc-length and the curvature of a parametric curve $\displaystyle \delta:\ I\rightarrow $\mathbb{R^2}$

Any help as to the steps involved greatly appreciated (running low on time before the exam day after tomorrow).

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- Jan 11th 2012, 03:27 PMmaxgunn555A straightforward question (but help needed!)
Recall how to calculate the arc-length and the curvature of a parametric curve $\displaystyle \delta:\ I\rightarrow $\mathbb{R^2}$

Any help as to the steps involved greatly appreciated (running low on time before the exam day after tomorrow). - Jan 11th 2012, 06:31 PMchisigmaRe: A straightforward question (but help needed!)
If the curvature is expressed in the form $\displaystyle y=f(x)\ ,\ a<x<b$, then the arc lenght is ...

$\displaystyle L= \int_{a}^{b} \sqrt{1+ (y^{'})^{2}}\ dx $ (1)

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$ - Jan 12th 2012, 02:26 PMmaxgunn555Re: A straightforward question (but help needed!)
Thanks.

I don't quite follow the 'y = f(x)'. i thought parametric curves looked like eg x = 2t +3, y = t^2 +2 e.t.c... - Jan 12th 2012, 07:35 PMchisigmaRe: A straightforward question (but help needed!)
If the curve is defined in parametric form $\displaystyle x=x(t)\ ,\ y=y(t)\ ,\ a<t<b$ , then ...

$\displaystyle L=\int_{a}^{b} \sqrt {[x^{'}(t)]^{2} + [y^{'}(t)]^{2}}\ dt$ (1)

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$ - Jan 13th 2012, 04:21 AMmaxgunn555Re: A straightforward question (but help needed!)
I'm sure now that's the formula i was looking for. Thanks A lot.