Find the length of the parametric curve described by \((x,y) = (2 \sin t, 2 \cos t)\) from \(t=0\) to \(t=\pi\)
+6248 \(\ell = \displaystyle \int \limits_0^\pi \sqrt{\dot{x}^2 + \dot{y}^2}~dt\\ \ell = \displaystyle \int \limits_0^\pi \sqrt{4\cos^2(t) + 4\sin^2(t)}~dt\\ \ell = \displaystyle \int \limits_0^\pi 2~dt = 2\pi\)
\(\text{in case you're not familiar with the notation $\dot{x} = \dfrac{dx}{dt}$}\)
.+6248 \(\ell = \displaystyle \int \limits_0^\pi \sqrt{\dot{x}^2 + \dot{y}^2}~dt\\ \ell = \displaystyle \int \limits_0^\pi \sqrt{4\cos^2(t) + 4\sin^2(t)}~dt\\ \ell = \displaystyle \int \limits_0^\pi 2~dt = 2\pi\)
\(\text{in case you're not familiar with the notation $\dot{x} = \dfrac{dx}{dt}$}\)
