Question

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

Answer #1

Find the area of the surface of revolution that is generated by
revolving the curve x= (y^4)/8 + (y^-2)/4, from y=2 to y=5, about
the line x=-1

Compute the surface area of the surface generated by revolving
the curve ?(?)=(?,??)c(t)=(t,et) about the ?-x-axis for 0≤?≤1.

Find the volume of the solid generated by revolving the region
bounded by the given curve and lines about the x-axis. y=4 square
root x, y=4 x=0

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)

Determine the surface area of a funnel that is generated by
revolving the graph of y = f(x) = x^3 + (1/12x) on the interval
from [1, 2] about the x-axis.

Find the volume generated by revolving the area in the first
quadrant bounded by the
curve y = e-x when the area is revolve about the line y
= -1 using the circular ring
method.

Consider the curve y = e sin x for π /6 ≤ x ≤ π /3 . Set up the
integrals (without evaluating) that represent
1. The area of the surface generated by revolving the curve
about the x-axis.
2. The area of the surface generated by revolving the curve
about the y-axis.

Find the volume of the solid generated by revolving
the area bounded by the given
curves/lines about the indicated axis using both vertical and
horizontal elements if applicable.
y=x² ,x=1, y=0
a. about the axis
b. about x=1
c. about the y-axis

Find the exact area of the surface obtained by rotating the
curve about the x axis.
1. Original problem y= x^3 from 0 < x < 2
I got up to the SA= 2 pi the integral of 1 to 145 of (x^3)(the
square root of (1+9x^4))dx
I don't know how to integrate from this part on to get the exact
answer.

Section 2 Problem 4:
a)Find the area of the surface obtained by rotating the
curvex=1/3((y^2)+2)^(3/2), 1<=y<=2, about the x-axis
b)Find the area of the surface generated by revolving the given
curve about the y-axis. x=sqrt(25-y^2), -4<=y<=4

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