解：联立y^2=2/3(x-1)^3和y^2=x/3得2(x-1)^3=x令x-1=t，得2t^3=t+12t^3-t-1=02t^3-2t+t-1=02t(t^2-1)+(t-1)=02t(t+1)(t-1)+(t-1)=0(t-1)[2t(t+1)+1]=0(t-1)(2t^2+2t+1)=0得t=1（2t^2+2t+1=0无解）故x=t+1=1+1=2,y=±√(2/3)=±√6/3半立方抛物线y^2=2/3(x-1)^3，两边对x求导得2y*dy/dx=2/3*3(x-1)^2=2(x-1)^2y'=dy/dx=(x-1)^2/y于是√(1+y'^2)=√[1+(x-1)^4/y^2]=√{1+(x-1)^4/[2/3*(x-1)^3}=√[(3x-1)/2]则该段圆弧长度L=2∫(x:0,2)√(1+y'^2)dx=2∫(x:1,2) √[(3x-1)/2]dx=2*√(3/2)*∫(x:1,2) √(x-1/3)dx=√6*2/3*(x-1/3)^(3/2)(x;1,2)=2(5√10-4)/9
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