Question

{F} Determine the length of the parametric curve given by the following parametric equations. x=3sin(t) y=3cos(t) 0<t<2π

Answer 1

$$dx/dt=3\cos(t), dy/dt=-3\sin(t)$$

$$L=\displaystyle\int_{0}^{2\pi}\sqrt{(dx/dt)^2+(dy/dt)^2}dt$$

$$=\displaystyle\int_{0}^{2\pi}\sqrt{(3\cos(t))^2+(-3\sin(t))^2}dt$$

$$=3\displaystyle\int_{0}^{2\pi}dt=3[t]\begin{matrix} 2\pi \\ 0 \end{matrix}=3(2\pi-0)=6\pi(units)$$

$$L=6\pi\ units$$