I need help with this question! (Vector Funtion problem)

Question

Find the arclength of the curve  r(t)= <2t^2, 2sqrt2, lnt>, for 1<= t <=4

Answer 1

Hi Grace, use this:

∫_a^bsqrt((dx/dt)^2+(dy/dt)^2+(dz/dt)^2) dt

That's the arc length for a parametric curve.

a=1

b=4

dx/dt=4

dy/dt=0 (unless that was 2√2t, which would be 2√2)

dz/dt=-1/t²

^{. Simplify and evaluate. I hope this helps!}