Note. In each example, the illustration shows the space curve. The part of the curve highlighted in red is the part whose length you are asked to find.
Find the length of r(t)=⟨cost,sint,t⟩ from t=−2 to t=2.
Find the length of v(t)=⟨12t,8t3/2,3t2⟩ from t=0 to t=1.
Find the length of r(θ)=cos3θi+sin3θj from θ=0 to θ=2π.
Find the length of r(u)=⟨1,−u2,u3⟩ from u=0 to u=1.