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 the arc length of the curve below on the given
interval.
Y = x^3+1/4x on [1,4]
I know the correct answer is 339/16, but I don't know how to get
there

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,...

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

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))

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

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

5.
(a) Find the length of the given line, C, using calculus and the
arc length formula:
C: ? = ? + 5 , 1 ≤ x ≤ 2
(b) Revolve the curve above, C, around the x-axis and find the
surface area of the resulting surface of revolution.

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