Find the length of the curve ⃗r(t) = ⟨ 1/3*t^3, t^2, 1⟩, 0 ≤ t ≤ 2.

r'(t) = <t^2, 2t,0>

|r'(t)| = sqrt( t^4 + 4t^2)

Arc length is integral of |r'(t)|, but how can i simplify it so i can integrate it?

Re: Find the length of the curve ⃗r(t) = ⟨ 1/3*t^3, t^2, 1⟩, 0 ≤ t ≤ 2.

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**linalg123** r'(t) = <t^2, 2t,0>

|r'(t)| = sqrt( t^4 + 4t^2)

Arc length is integral of |r'(t)|, but how can i simplify it so i can integrate it?

Integral , click "show steps"

Re: Find the length of the curve ⃗r(t) = ⟨ 1/3*t^3, t^2, 1⟩, 0 ≤ t ≤ 2.

$\displaystyle \int_0^2 \sqrt{t^4+4t^2}dt = \int_0^2 t \sqrt{t^2+4} dt$

make the substitution $\displaystyle u = t^2 + 4 $

and the integral should be easy.