Question

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

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).

1. a) Get the arc length of the curve.
r(t)= (cos(t) + tsin(t), sin(t) - tcos(t), √3/2 t^2) in
the Interval 1 ≤ t ≤ 4
b) Get the curvature of r(t) = (e^2t sen(t), e^2t, e^2t cos
(t))

Write the curve given by r(t)=((3/2)t)i+(t^3/2)j as a function
r(s) parameterized by the arc length s from the point where t=0.
Write your answer using standard unit vector notation.

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

Parameterize the curve using the arc-length parameter s, at the
point at which t=0t=0 for r(t)=e^tsint i+e^tcost j.

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

Find the length of the curve
1) x=2sin t+2t, y=2cos t, 0≤t≤pi
2) x=6 cos t, y=6 sin t, 0≤t≤pi
3) x=7sin t- 7t cos t, y=7cos t+ 7 t sin t, 0≤t≤pi/4

Consider the curve r(t) = cost(t)i + sin(t)j +
(2/3)t2/3k
Find:
a. the length of the curve from t = 0 to t = 2pi.
b. the equation of the tangent line at the point t = 0.
c. the speed of the point moving along the curve at the point t
= 2pi

18. Find aT at time t=2 for the space curve r(t)= (9t-1)i + t^2
j -8tk

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.

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