philosphy111of

2021-11-16

Find the length of the curve.

$r\left(t\right)=4t,{t}^{2},{t}^{3},\text{}0\le t\le 1$

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

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

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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