Answer to Question #284260 in Calculus for Amit

Question #284260

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


1
Expert's answer
2022-01-17T18:01:52-0500

Solution

For given parametric equations

L=02π(dxdt)2+(dydt)2dt=02π(3cos(t))2+(3sin(t))2dt=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=}

=302πcos(t)2+sin(t)2dt=302πdt=6π=3\int_{0}^{2\pi}{\sqrt{{cos(t)}^2+{sin(t)}^2}dt=}3\int_{0}^{2\pi}dt=6\pi


Answer

L=6π



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