Question

1. Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the line x=4.

y=x^2 y=4x-x^2

2. Use the disk or shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the region bounded by the graphs of the equations about each given line.

y=x^3 y=0 x=2

a) x-axis b) y-axis c) x=4

Answer #1

Set up the integral (do not evaluate) to find the volume of the
solid generated by revolving the region about the line x=5.
The region is bounded the graphs x=y^2, x=4
Use the disk and shell methods.

Set up an integral using the shell method to find the volume of
the solid generated by revolving the area bounded by the graphs of
the equations y=1/(x+2) y =0, x = 0 and x=5 about the line x=
-3.Sketch a graph of the region, highlighting your slice

Use a detailed analysis to set up but not evaluate an integral
for the volume Z of the solid generated by revolving the region
bounded by the curves 2x = y^2, x = 0, and y = 4 about the
y-axis.

Use the shell method to find the volume of the solid generated
by revolving the plane region about the line x = 4.
y = x2
y = 4x − x2

#6) a) Set up an integral for the volume of the solid S
generated by rotating the region R bounded by x= 4y and y= x^1/3
about the line y= 2. Include a sketch of the region R. (Do
not evaluate the integral).
b) Find the volume of the solid generated when the plane region
R, bounded by y^2= x and x= 2y, is rotated about the
x-axis. Sketch the region and a typical shell.
c) Find the length of...

Using any method, SET UP, but do NOT evaluate, an integral
representing the volume of the solid obtained by rotating the
region bounded by the curves y = 1 x , y = 0, x = 1, x = 3 about
(a) the line y = −1 (b) the y-axis.

Using any method, SET UP, but do NOT evaluate, an integral
representing the volume of the solid obtained by rotating the
region bounded by the curves y = 1/x , y = 0, x = 1, x = 3 about
(a) the line y = −1 (b) the y-axis

Use the shell method to find the volume of the solid generated
by revolving the region bounded by the given curves about the give
line. (a) Graph the region (b) Graph the solid (c) Sketch a typical
shell. (d) Determine the variable of integratoin (e) Draw and label
the radius and height of the shell. Describe their length. (f) Find
the volume.
y = 4x, y = 0, x = 2; revolve about the line x = -3

Use shell method to find the volume of the solid generated by
revolving the region bounded by y=4−x, y=2 ,x=0 about x-axis.
Sketch the region.

Use the shell method to find the volume of the solid generated
by revolving the region bounded by y=3x-2, y=sqrt.x, and x=0 about
the y-axis.
The volume is in cubic units.

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