Find the length of the curve. r(t)=4t,t^2,t^3,\ 0\leq t\leq1



Answered question


Find the length of the curve.
r(t)=4t,t2,t3, 0t1

Answer & Explanation

Julie Mathew

Julie Mathew

Beginner2021-11-17Added 15 answers

To find the length of the given parametric curve
Length formula for the parametric curve with prescribed limits
If r(t)=(f(t),g(t),h(t)), atb
then, L =length of the parametric curve segment
Now, this integral cannot be evaluated in a closed form, as the integrand is not the derivative of a closed expression
Given r(t)=(4t,t2,t3), atb
So, L can be estimated by a suitable numerical procedure, say , Simpson's formula: The approximate value of L is found to be 4.36

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