Adapted by Mrs. King from
http://tutorial.math.lamar.edu/AllBrowsers/2413/VolumeWithRings.asp
Disc Method:
What if the “slices” aren’t solid?
pigsflyguy.com/sitebuildercontent/sitebuilderfiles/sec_07_02_washer_method.ppt
Washers!
Washers
 Consider the area between two functions
rotated about the axis
 Now we have a hollow solid
 We will sum the volumes of washers
f(x)
g(x)
a
b
Washers
b
V 
 f (x)   g(x) dx
a
Outer
Function
2
f(x)
g(x)
2
a
Inner
Function
b
The Method of Washers
 Find the volume of
the solid formed by
revolving the region
bounded by y = (x)
and y = x² over the
interval [0, 1] about
the x – axis.
glory.gc.maricopa.edu/~avolpe/230page/7.2calc2discsnadwashers.ppt
Solution:b
V    ([ f ( x)]  [ g ( x)] )dx
2
a
1
V  
0
2
 x   x  dx
2
1

2 2

V    x  x dx
0
4
 1 2 1 5   3
V   x  x 
10
5 0
2
1
Homework
 Page 465
 #5, 6, 13a, 14a
http://mathdemos.gcsu.edu/mathdemos/washer
method/gallery/gallery.html