<P>x(t)=cost i +sint j +t k</P> <P>상의 점 (1,0,0)에서 (1,0,2<COMMENT class=MATH>[0]#wh4/3.4`4.7/12,[1]{pi}</COMMENT>)까지의 길이를 구하여라.</P> <P> </P> <P>이문제에서.</P> <P>그림삽입이 필요한데..</P> <P>GSP로해서 점의 변화에따른 상나선의 길이 변화도 </P> <P>학생들이 직접 해볼수 있도록 하려니..</P> <P>너무 어렵네요..</P> <P> </P> <P>풀이))</P> <P>x'(t)=-sint i+cost j +k,</P> <P>|x'(t)|=<COMMENT class=MATH>[0]#wh4/44.7`6.9/12,[1]{sqrt{({(-sint)}^{2}`plus`{(cost)}^{2}`plus`{1}^{2})}}</COMMENT>=<COMMENT class=MATH>[0]#wh4/5.4`5.3/12,[1]{sqrt{2}}</COMMENT></P> <P>따라서 점(1,0,0)에서 (1,0,2<COMMENT class=MATH>[0]#wh4/3.4`4.7/12,[1]{pi}</COMMENT>)까지는 0<COMMENT class=MATH>[0]#wh4/4.4`4.7/12,[1]{`leq`}</COMMENT>t<COMMENT class=MATH>[0]#wh4/4.4`4.7/12,[1]{`leq`}</COMMENT>2<COMMENT class=MATH>[0]#wh4/3.4`4.7/12,[1]{pi}</COMMENT>에 해당하므로</P> <P>곡선의 길이는</P> <P>l=<COMMENT class=MATH>[0]#wh4/7`15.1/12,[1]{int_{0}^{2`pi}}</COMMENT>|x'(t)|dt=<COMMENT class=MATH>[0]#wh4/7`15.1/12,[1]{int_{0}^{2`pi}}</COMMENT><COMMENT class=MATH>[0]#wh4/5.4`5.3/12,[1]{sqrt{2}}</COMMENT>dt=2<COMMENT class=MATH>[0]#wh4/5.4`5.3/12,[1]{sqrt{2}}</COMMENT><COMMENT class=MATH>[0]#wh4/3.4`4.7/12,[1]{pi}</COMMENT>.</P>
