What is the arclength of #f(t) = (e^(t)-e^(t^2)/t,t^2-1)# on #t in [1,3]#? Calculus Parametric Functions Determining the Length of a Parametric Curve (Parametric Form) 1 Answer Sonnhard Jun 23, 2018 #approx 2681.58# Explanation: With #x(t)=e^t-e^(t^2)/t# we get #x'(t)=e^t-2e^(t^2)+e^(t^2)/t^2# #y(t)=t^2-1# so #y'(t)=2t# and we have to solve #int_1^3sqrt((e^t-2e^(t^2)+e^(t^2)/t)^2+(2t)^2)dt approx 2681.58# 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 1348 views around the world You can reuse this answer Creative Commons License