x=3cos^3t, y=3sin^3t, t принадлежит [0, pi/2]
y`_(t)=9sin^2t*(cost)
(x`_(t))^2+(y`_(t))^2=81cos^4t*sin^2+81sin^4t*cos^2t=81sin^2t*cos^2t(cos^2t+sin^2t)=81sin^2t*cos^2t
sqrt((x`_(t))^2+(y`_(t))^2)=sqrt(81sin^2t*cos^2t)=9*sint*cost
L= ∫ ^(pi/2)_(0)9*sint *[b]cost[/b][b]dt[/b]=9∫ ^(pi/2)_(0)sint [b]d(sint)[/b]=9(sin^2t/2)|^(pi/2)_(0)=(9/2)*(1-0)=9/2