Question

The region bounded by y=2^x and y=4x-4 is rotated about the line y=3. Find the volume of the resulting solid.

Answer #1

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1. The region bounded by y=x8 and y=sin(πx/2) is
rotated about the line x=−7.
Using cylindrical shells, set up an integral for the volume of the
resulting solid.
2.The region bounded by y=9/(1+x2), y=0, x=0 and x=8
is rotated about the line x=8.
Using cylindrical shells, set up an integral for the volume of the
resulting solid.

The region bounded by the given curves is rotated about the
specified axis. Find the volume V of the resulting solid
by any method.
x = (y −
9)2, x =
16; about y = 5
V =

The region in the first quadrant bounded by y=2x^2 ,
4x+y=6, and the y-axis is rotate about the line
x=−3.
The volume of the resulting solid is:

consider the region r bounded by the parabola y=4x^2 and the
lines x=0 and y=16 find the volume of the solid obtained by
revolving R about the line x=1

3. Find the volume of the solid of revolution. The region is
bounded by y= 4x and y = x^3 and x ≥ 0.
a) Make a sketch.
b) About the x axis (disk/washer method).
c) About the x axis (cylindrical shells).
d) About the y axis (disk/washer method).
e) About the y axis (cylindrical shells).

Consider the region bounded by y=2x and y=x^2. Rotate it about
the Y-axis. Find the volume of the resulting solid.

40) The region bounded by f(x)=−2x^2+12x+32, x=0 and y=0 is
rotated about the y-axis. Find the volume of the solid of
revolution.
Find the exact value; write answers without decimals.

1) A volume is described as follows:
1. the base is the region bounded by y=2−2/25x^2 and y=0
2. every cross-section parallel to the x-axis is a
triangle whose height and base are equal.
Find the volume of this object.
volume =
2) The region bounded by f(x)=−4x^2+24x+108, x=0, and y=0 is
rotated about the y-axis. Find the volume of the solid of
revolution.
Find the exact value; write answer without decimals.

Find the volume of the solid generated by revolving the region
bounded by y = sqrt(x) and the lines and about y=2 and x=0
about:
1) the x-axis.
2) the y-axis.
3) the line y=2.
4) the line x=4.

What is the volume of the solid obtained by rotating the region
bounded by the
curves y = −x^2 + 4x − 3 and y = 0 rotated about the y-axis?

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