What is the arclength of #f(t) = (t^3-t^2+5t,9t)# on #t in [1,4]#? Calculus Parametric Functions Determining the Length of a Parametric Curve (Parametric Form) 1 Answer Douglas K. Sep 27, 2016 Use #L = int_1^4 (sqrt(((d(x(t)))/dt)^2 + ((dy(t))/dt)^2))dt# where #x(t) = t^3 - t^2 + 5t# and #y(t) = 9t# Explanation: #L = int_1^4 (sqrt((3t^2 - 2t + 5)^2 + 9^2))dt# #L ~~ 70.05 # 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 1206 views around the world You can reuse this answer Creative Commons License