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Calculus Applications of Integration Page
13
Applications of Integration Day 4
Volume formulas for rotation around the axes (based on crosssectional areas):
Disk
Washer
f(x) around the xaxis
region between f(x) and g(x) around xaxis
f(y) around the yaxis
region between f(y) and g(y) around yaxis
More Volumes using the Washer Method
Example 1
(1985 exam)
The region bounded by the curves
y
=
e
x
and
y
=
e
−
x
is rotated about the xaxis
to generate a solid.
Find the volume of the solid.
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14
Example 2
Find the volume of the solid generated by revolving the region bounded
y
=
x
2
and
y
=
2
x
about the yaxis
Rotating Regions about lines parallel to the axes.
First idea – think of distances in terms of x and y values
Graph
y
=
x
2
below and pick a point (x, y).
Consider distances from the point to
the lines y=3 and y=–1.
Then consider distances from point to the lines x = 2 and
x = –2
Calculus Applications of Integration Page
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Example 3
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This note was uploaded on 02/04/2011 for the course MATH 116 taught by Professor John during the Spring '10 term at St. Michael.
 Spring '10
 John
 Calculus, Formulas

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