Define a parametric curve and the parametric interval using parameter [math]t[/math]. As you move the slider, the curve is traced out, and you'll see a red dot indicating the centroid of the curve. [br][br]Suppose curve [math]C[/math] is given by [math]x=x\left(t\right)[/math], [math]y=y\left(t\right)[/math] for [math]a\le t\le b[/math]. [br]For convenience, take [math]\frac{ds}{dt}=\sqrt{\left(\frac{dx}{dt}\right)^2+\left(\frac{dy}{dt}\right)^2}[/math].[br]Then the centroid of [math]C[/math] is [math]\left(\overline{x},\overline{y}\right)[/math] where:[br] [math]L=\int_a^b\frac{ds}{dt}dt[/math] [math]\overline{x}=\frac{1}{L}\int_a^bx\frac{ds}{dt}dt[/math] [math]\overline{y}=\frac{1}{L}\int_a^by\frac{ds}{dt}dt[/math]

[i]This applet was developed for use with [url=https://www.pearson.com/en-us/subject-catalog/p/interactive-calculus-early-transcendentals-single-variable/P200000009666]Interactive Calculus[/url], published by Pearson.[/i]