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).
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).
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
$\displaystyle \chi$ $\displaystyle \sigma$
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
$\displaystyle \chi$ $\displaystyle \sigma$