Question

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.

Answer #1

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/ The Arc Of The Parabola Y= Sqrt(x-6) From X=7 To X= 15 Is Rotated
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arc of the parabola y= sqrt(x-6) from x=7 to x= 15 is rotated about
the x-axis find the area ... the arc of the parabola y= sqrt(x-6)
from...

for a and b use x= Square root x
and g(x)=x/2
a) Find the arc length of the
curve of f(x) for
0≤x≤4.
b) Find the surface area of the
solid of revolution revolved about the x-axis of
f(x) for 0≤x≤4.

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,...

1) Find the arc length of the graph of the
function over the indicated interval. Show your work.
y=ln(cosx) ; [ 0 ,
π/4]
2)
Find the surface area generated by revolving
the graph about the x - axis over the indicated interval. Show your
work.
y=2x ; [ 0 , 3
]

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

I have some integration questions for calc homework
1. Compute ds (the differential of arc length) for f(x) = 2^x
.
2. Compute the arc length of f(x) = 9x ^ 2/3 over the interval
[0, 1].
3. Find the surface area of the hollow shape obtained by
rotating f(x) = sin(x) from x = 0 to x = π about the x-axis.
Thanks for any help!

a) Find the arc length parametrization of the line x=-2+4t,
y=3t, z=2+t that has the same direction as the given line and has
reference point (-2,0,2).
Use an arc length S as a parameter. x= y= z= b) Use the
parametric equations obtained in part (a) to find the point on the
line that is 20 units from the reference point in the direction of
increasing parameter.
x=
y=
z=
b) Use the parametric equations obtained in part (a) to...

The given curve is rotated about the y-axis. Find the
area of the resulting surface.
y =
3
x
, 3 ≤ y ≤ 5

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

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