Question

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

Answer #1

Answer 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.

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

5.
Find a general solution of t^2x′′ − 5tx′ + 5x = 6t^3, t > 0
using the method of undetermined coefficients

. 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 solution to the following ivp
dy/dy-2ty=6t^2e^(t^2),y(0)=5

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

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

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

4.
Find a general solution of t^2x′′ − 5tx′ + 5x = 6t^3, t > 0
using the method of variation of parameters.

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