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z9YVs+KuuVjT}#SI295{8+0&Zmk#X2lWdR%Z30g>h6VU22hF>3gnSXEAH)w&=lkl_V zp8hUr=Clb~IQ|!|BH6uaUa@%Ebn@aMs&>S!QMWp<=_Jw_wz}ctVUOFNm>xq7+b5LYl#jtNNHu34gfc0Mj$j30_j?8X0AL~bCjiNV?v z8~`90*}o~(fAPx(ccyrx?6*_Mv_g zY;f>G^QCgSC$wg+92K%26>?WA61E|Moc*9M(bzIi-QJ`;++{n51nv5LOxYPcrfrHF z!dhcL09RT!OeSXJ = 0\\ +\\ +G = ||s_v||^2 = r^2\\$ +\\ +$\Rightarrow I_{\tau}^f = \begin{pmatrix} (r(cos(u))+R)^2 & 0 \\ 0 & r^2 \end{pmatrix}$ + +\subsection*{c)} + +Aus der Vorlesung: $dA = \sqrt{det I_{\tau}^f} \,du\,dv$\\ +\begin{align*} +\Rightarrow dA &= \sqrt{det \begin{pmatrix} (r(cos(u))+R)^2 & 0 \\ 0 & r^2 \end{pmatrix}} \,du\,dv\\ +\Rightarrow dA &= r(r(cos(u))+R) \,du\,dv\\ +\end{align*} +\\ +$\Rightarrow A = \int_{0}^{2\pi} \int_{0}^{2\pi} r(r(cos(u))+R) \,du\,dv = 2 \pi r \times \int_{0}^{2\pi} r(cos(u))+R \,dv =\\\\ 2 \pi r [Rv + r(sin(v)]_{0}^{2\pi} = 2 \pi r \times (2\pi R) = \underline{\underline{4\pi^2Rr}} $ +t\end{document} +