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50 1 A n w e n d u n g e n der Differential- u n d I n t e g r a l r e c h n u n g b) F l ä c h e n i n h a l t der v o n einem Z y k l o i d e n b o g e n u n d der x-Achse b e r a n d e t e n F l ä c h e D u r c h x = R(t — sin t\ y = R(l — cos t) m i t te[0,2n\ wird ein Z y k l o i d e n b o g e n b e s c h r i e b e n (vgl. 5). ): o [R(t - sin t)R sin t - R{1 - cos t)R(l - cos £)] dt A = \ \ R = — j (t-sin t — s i n 1 — 1 + 2 cos t — c o s 1 ) dt R R J [t• sin t + 2(cos t - 1)] dt = — [sin t - t• cos t + 2 sin t - 2t] ° 2 0 2 2 2 0 2 2n R 2 - [ - ( - 2 7 i - 4 7 i ) ] = 37i# .

N) aus, d e n e n P u n k t e P = (x , y^) mit y = f(x ) auf der K u r v e e n t s p r e c h e n (s. 25). 25, B a n d 1) in allen Intervallen (x _ ,x ) Zwischenstellen £ mit: i AR,. ) Ax,. Y,. x -x . i i 1 i t ,| 1 D a m i t h a t d e r z u r Z e r l e g u n g Z gehörige S t r e c k e n z u g die L ä n g e n i= X 1 ) AUF ÄHNLICHE WEISE WURDE IN ABSCHNITT 9 . 1 . 1 , BAND 1 DER BEGRIFF FLÄCHENINHALT MIT HILFE DER BEKANNTEN RECHTECKFLÄCHEN ERKLÄRT. 1, B a n d 1 d e r G r e n z w e r t lim £ g(

E n d k n o t e n a b h ä n g t . Bemerkung: W e i t e r e V o r s c h l ä g e z u r W a h l der R a n d b e d i n g u n g e n findet m a n in der einschlägigen L i t e r a t u r . 29 W i r b e s t i m m e n die k u b i s c h e S p l i n e - K u r v e S d u r c h die 5 K n o t e n P , P . . , P 0 a) n a t ü r l i c h e n R a n d b e d i n g u n g e n , b) d e n R a n d b e d i n g u n g e n T = ~a 0 0 und l 5 4 zu T =

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