求圆x=a(cost+tsint),y=a(sint-tcost)的渐伸线的弧长
问题描述：
求圆x=a(cost+tsint),y=a(sint-tcost)的渐伸线的弧长
答
x'(t)=a(-sint+sint+tcost)=atcost,y'(t)=a(cost-cost+tsint)=atsint,x'(t)^2+y'(t)^2=a^2t^2,s=∫ [0,2π] √ [x'(t)^2+y'(t)^2]dt=∫ [0,2π] (at)dt=a(t^2)/2[0,2π]=2π^2a.∴圆的渐开线一周弧长为2π^2a....