Answer to Question #284260 in Calculus for Amit

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

Solution

For given parametric equations

$L=\int_{0}^{2\pi}{\sqrt{\left(\frac{dx}{dt}\right)^2+\left(\frac{dy}{dt}\right)^2}dt=}\int_{0}^{2\pi}{\sqrt{\left(3cos(t)\right)^2+\left(-3sin(t)\right)^2}dt=}$

$=3\int_{0}^{2\pi}{\sqrt{{cos(t)}^2+{sin(t)}^2}dt=}3\int_{0}^{2\pi}dt=6\pi$

Answer

L=6π