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.
Quote:
Originally Posted by
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.
make the substitution 
and the integral should be easy.
