Question

Find the arc length of the given curve on the specified interval, (t, t, t2), for 1 ≤ t ≤ 2

Answer #1

Find the arc length of the curve on the given interval. (Round
your answer to three decimal places.)
Parametric Equations
Interval
x = 6t + 5, y = 7 − 5t
−1 ≤ t ≤ 3

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.

Find the arc length function for the curve with the given
starting point
y=14x3/2,P0(1,14)

Find the exact length of the curve. x = 8 + 9t2, y = 3 + 6t3, 0
≤ t ≤ 5
Find an equation of the tangent to the curve at the given point
by both eliminating the parameter and without eliminating the
parameter. x = 6 + ln(t), y = t2 + 1, (6, 2) y =
Find dy/dx. x = t 3 + t , y = 3 + t
Find the distance traveled by a particle...

Find the arc length
? = 1/2(? ^3/2) − 1
interval [2,6]

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.

Consider the parametric curve given by x ( t ) = e t c o s ( t )
, y ( t ) = e t s i n ( t ) , t ≥ 0.
Find the arc-length of this curve over the interval 0 ≤ t ≤
3.

Consider the parametric curve
x = t2, y = t3 + 3t, −∞ < t < ∞.
(a) Find all of the points where the tangent line is
vertical.
(b) Find d2y/dx2 at the point (1, 4).
(c) Set up an integral for the area under the curve from t = −2
to t = −1.
(d) Set up an integral for the length of the curve from t=−1 to
t=1.

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

For the curve x = sint - tcost, y = cost + tsint, z =
t2
find the arc length between (0, 1, 0) and (-2π, 1,
4π2)
I have gotten down to tsqrt(5) but how am I supposed to assign
the bounds given 3 variables in space and not only 2?

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