Question

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

Answer #1

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

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.

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.

Find the volume of the solid generated by revolving the plane
region bounded by the graphs of y= \sqrt{x} , y=0, x=5, about the
line x=8.
Find the volume using: a) DISK/WASHER Method b) SHELL METHOD

Find the volume of the solid generated by revolving the plane
region bounded by the graphs of y= \sqrt{x} , y=0, x=5, about the
line x=8.
Find the volume using: a) DISK/WASHER Method b) SHELL METHOD

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.

Use the shell method to find the volume of the solid generated
by revolving the region bounded by the given curves and lines about
the y-axis.
y = x 2 - 4, y = 3x, x = 0, for x ≥ 0

Using the Shells method, find the volume of the solid generated
by revolving the region bounded by
y = 5 - x, y = 0, x = 0
about the line y = -1.

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

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