Consider the parametric equation #x= 10(cost+tsint)# and #y= 10(sint-tcost)#, What is the length of the curve from #0# to #((3pi)/2)#? Calculus Parametric Functions Determining the Length of a Parametric Curve (Parametric Form) 1 Answer Cesareo R. Nov 16, 2016 #10/2((3pi)/2)^2# Explanation: #{(x = 10 (Cos t + t Sint)),(y=10 (Sint - t Cost)):}# #(ds)/dt = sqrt(((dx)/dt)^2+((dy)/dt)^2# #dx/dt=10tcost# #dy/dt=10t sint# #(ds)/dt=10t# #s=int_(t=0)^((3pi)/2)10tdt = 10/2((3pi)/2)^2# Answer link Related questions How do you find the arc length of a parametric curve? How do you find the length of the curve #x=1+3t^2#, #y=4+2t^3#, where #0<=t<=1# ? How do you find the length of the curve #x=e^t+e^-t#, #y=5-2t#, where #0<=t<=3# ? How do you find the length of the curve #x=t/(1+t)#, #y=ln(1+t)#, where #0<=t<=2# ? How do you find the length of the curve #x=3t-t^3#, #y=3t^2#, where #0<=t<=sqrt(3)# ? How do you determine the length of a parametric curve? How do you determine the length of #x=3t^2#, #y=t^3+4t# for t is between [0,2]? How do you determine the length of #x=2t^2#, #y=t^3+3t# for t is between [0,2]? What is the arc length of #r(t)=(t,t,t)# on #tin [1,2]#? What is the arc length of #r(t)=(te^(t^2),t^2e^t,1/t)# on #tin [1,ln2]#? See all questions in Determining the Length of a Parametric Curve (Parametric Form) Impact of this question 5699 views around the world You can reuse this answer Creative Commons License