Question

Determining Volumes by the Disk-Washer Method

1. Find the volume of the solid formed by revolving the region bounded by the graph of f(x) = √sin(x) and the x−axis from 0 ≤ x ≤ π about the x−axis. [f(x)= square root(sin(x))]

Answer #1

Using the disk or washer method, find the volume of the solid
generated by revolving the region bounded by y = x 2 + 1 and y = x
+ 3, about the line y = −1.

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 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.

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

Find the volume of the solid generated by revolving the region
bounded by the graphs of y = e x/4 , y = 0, x = 0, and x = 6 about
the x−axis.
Find the volume of the solid generated by revolving the region
bounded by the graphs of y = √ 2x − 5, y = 0, and x = 4 about the
y−axis.

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

find the volume of the solid generated by revolving the region
about the axis. use the shell or washer method. the region in the
first quadrant bounded by x=2y-y^2 and the y-axis about the
x-axis
a) 8/3 pi
b) 4pi
c) 4/3 pi
d) 2pi
which choice is the correct?

3.
(a) Find the volume of the solid generated by revolving the
region bounded by the graphs of the given equations around the
x-axis.
? = 0, ? = ? 3 + ?, ? = 1
(b) Find the volume of the solid generated by revolving the
region from part (a) around the y-axis

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