6'1 Areas Between Curves

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6.1 Areas Between Curves
Suppose we want to find the area of the region S
as shown in Figure 1.
y
f
S
g
x
b
Figure 1
a
2
y
f
g
x
a
b
Figure 2
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When the graph of the area of the region is
already determined, it is often convenient to use
a typical approximating rectangle (strip) to
write the integration formula for the area
between two curves. In general, we use
Vertical Strips (of width ) implies
integration with respect to x
in variable x
Horizontal Strips (of width ) implies
integration with respect to y
in variable y
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Examples Sketch the region bounded by the given
curves and find the exact area of the
region. Example One Example Two
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Solutions Example One Find the points of
intersection of the graphs
y
(2,1)
x
(-1, -2)
The area is
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Solutions Example Two
Find the points of intersection of the two
curves
y
1
x
The total area is
0