Hallo,
\( L=\int \limits_{0}^{3 \pi} \sqrt{x^{\prime 2}+y^{\prime 2}} d t \)
also 1. Ableitung bilden , quadrieren und ausrechnen
=\( \int \limits_{0}^{3 \pi} \sqrt{1+t^{2}} d t \)
=\( \int \sqrt{1+t^{2}} d t=\frac{1}{2}\left(\sqrt{t^{2}+1} t+\sinh ^{-1}(t)\right)+ \) constant
=\( \int \limits_{0}^{3 \pi} \sqrt{1+t^{2}} d t=\frac{1}{2}\left(3 \pi \sqrt{1+9 \pi^{2}}+\sinh ^{-1}(3 \pi)\right) \approx 46.132 \)
