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# help

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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

#1
+6046
+1

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

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

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Aug 20, 2019

#1
+6046
+1

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

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

Rom Aug 20, 2019