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Find the length of the parametric curve described by  \((x,y) = (2 \sin t, 2 \cos t)\) from \(t=0\) to \(t=\pi\)

 Aug 20, 2019

Best Answer 

 #1
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\(\ell = \displaystyle \int \limits_0^\pi \sqrt{\dot{x}^2 + \dot{y}^2}~dt\\ \ell = \displaystyle \int \limits_0^\pi \sqrt{4\cos^2(t) + 4\sin^2(t)}~dt\\ \ell = \displaystyle \int \limits_0^\pi 2~dt = 2\pi\)

 

\(\text{in case you're not familiar with the notation $\dot{x} = \dfrac{dx}{dt}$}\)

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 Aug 20, 2019
 #1
avatar+6045 
+1
Best Answer

\(\ell = \displaystyle \int \limits_0^\pi \sqrt{\dot{x}^2 + \dot{y}^2}~dt\\ \ell = \displaystyle \int \limits_0^\pi \sqrt{4\cos^2(t) + 4\sin^2(t)}~dt\\ \ell = \displaystyle \int \limits_0^\pi 2~dt = 2\pi\)

 

\(\text{in case you're not familiar with the notation $\dot{x} = \dfrac{dx}{dt}$}\)

Rom Aug 20, 2019

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