Question

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.**

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

A) Use the arc length formula to find the length of the
curve
y = 2x − 1,
−2 ≤ x ≤ 1.
Check your answer by noting that the curve is a line segment and
calculating its length by the distance formula.
B) Find the average value fave of the
function f on the given interval.
fave =
C) Find the average value have of the
function h on the given interval.
h(x) = 9 cos4 x sin x, [0,...

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 exact length of the curve.
y = ln(sec x), 0 ≤
x ≤ π/3

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 the given curve on the specified
interval, (t, t, t2), for 1 ≤ t ≤ 2

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

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

Find the arc length (exact value) of the polar curve r = 2sintheta
+ 4 costheta.
0 <= theta <= 3pi/4 by setting up and evaluating a
definite integral.

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