Question

Find the arc length of r(t) = from (1,0,0) to (-1,2,0)

Answer #1

. Find the arc length of the curve r(t) = <t^2 cos(t), t^2
sin(t)> from the point (0, 0) to (−π^2 , 0).

Find an arc length parametrization of
r(t) =
(et
sin(t),
et
cos(t),
10et )

Find the arc length of the curve r(t) = i + 3t2j +
t3k on the interval [0,√45].
Hint: Use u-substitution to integrate.

Find an arc length parametrization of r(t)=<3t^2,
2t^3>.
r(g(s))=<_______________, +-____________________>

Find, for 0 ≤ x ≤ π, the arc-length of
the segment of the curve R(t) = ( 2cost − cos2t, 2sint −
sin2t )
corresponding to 0 ≤ t ≤ x.

Parametrize the curve r(t) = <5sin(t), 5cos(t), 12t> with
respect to arc length, measured from the point (0,5,0).

Find the curvature of the curve r(t) = <etcos(t),
etsin(t), t> at the point (1,0,0)

Find the arc length of r = θ 2 from θ = 2π to θ = 6π.

Calculate the arc length of the indicated portion of the curve
r(t).
r(t) = 6√2 t^((3⁄2) )i + (9t sin t)j + (9t cos t)k ; -3 ≤ t ≤
7

Find the arc length of a(t)=(2cosh3t,-2sinh3t,6t) for 0≤t≤5

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