# A 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}$Any help as to the steps involved greatly appreciated (running low on time before the exam day after tomorrow). • Jan 11th 2012, 06:31 PM chisigma Re: A straightforward question (but help needed!) If the curvature is expressed in the form$\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$• Jan 12th 2012, 02:26 PM maxgunn555 Re: A straightforward question (but help needed!) Thanks. I don't quite follow the 'y = f(x)'. i thought parametric curves looked like eg x = 2t +3, y = t^2 +2 e.t.c... • Jan 12th 2012, 07:35 PM chisigma Re: A straightforward question (but help needed!) If the curve is defined in parametric form$\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\$