Home > Calculus > Determining the Length of a Parametric Curve (Parametric Form)

What is the arclength of #f(t) = (e^(t)-e^(t^2)/t,t^2-1)# on #t in [1,3]#?

Answer 1

Christopher Agresta

#approx 2681.58#

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#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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