[r]L= ∫ ^(t_(2))_(t_(1)) sqrt((x`(t))^2+(y`(t))^2)dt[/r]
x`(t)=(cost+tsint)`=(cost)`+t`*sint+t*(sint)`=-sint+sint+t*cost=t*cost
y`(t)=(sint-tcost)`=(sint)`-t`*cost-t*(cost)`=cost-cost-t*(-sint)=t*sint
(x`(t))^2+(y`(t))^2=t^2cos^2t+t^2sin^2t=t^2(sin^2t+cos^2t)=t^2*1=t^2
sqrt((x`(t))^2+(y`(t))^2)=t
L= ∫ ^(π/4)_(0) tdt=(t^2/2)|^(π/4)_(0)=[b]π^2/32[/b]