Question

*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*.

Answer #1

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.

Find the area of the surface generated by revolving the curve x
= ?square root 4y − y2, 1 ≤ y ≤ 2, about y-axis.

A. For the region bounded by y = 4 − x2 and the x-axis, find
the volume of solid of revolution when the area is revolved
about:
(I) the x-axis,
(ii) the y-axis,
(iii) the line y = 4,
(iv) the line 3x + 2y − 10 = 0.
Use Second Theorem of Pappus.
B. Locate the centroid of the area of the region bounded by y
= 4 − x2 and the x-axis.

a.) Find the length of the curve y=ln(x),1 ≤ x ≤ sqrt(3)
b.) Using disks or washers, find the volume of the solid
obtained by rotating the region bounded by the curves y^2=x and
x=2y about the y-axis
c.) Find the volume of the solid that results when the region
bounded by x=y^2 and x=y+12 is revolved about the y-axis

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
]

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) 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,...

2. Rotate the semicircle of radius 2 given by y = √(4 − x^2)
about the x-axis to generate a sphere of radius 2, and use this to
calculate the surface area of the sphere.
3. Consider the curve given by parametric equations x = 2
sin(t), y = 2 cos(t).
a. Find dy/dx
b. Find the arclength of the curve for 0 ≤ θ ≤ 2π.
4.
a. Sketch one loop of the curve r = sin(2θ) and find...

Find the area of the surface generated when the given curve
is revolved about the y-axis.
The part of the curve y= 1/2ln (2x + square root of
4x2 - 1 )between the pointe
(1/2,0) and (17/16,ln
2)

To find the square root of x, make a guess g. If g**2 is close
enough to x, then report g as the square root. Otherwise, make a
new guess which is the average of g and x/g. Check the new guess
and keep repeating until the square of the guess is close enough to
x. Suppose x is 99 and the first guess is 5. Using this algorithm,
how many guesses will it take until the guess squared is...

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