13.3 Area - 1 3 .3 
A r e a 

 


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Unformatted text preview: 1 3 .3 
A r e a 

 
 Def:

The
area
of
a
closed
bounded
plane
region
R
is
 ∫∫ 1 R dA 
 
 Ex.

Find
the
area
of
the
region
bounded
by
 x= 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 12 y − 3 and x − y = 1.
 2 Def:

The
average
value
of
f
over
R
is
 1 area of R ∫∫ f R dA 
 
 Ex.
Find
the
average
value
of
f(x,
y)
=
x
+
y
over
the
region

 O
≤
x
≤
3
and
0
≤
y
≤
2.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Ex.
Find
the
average
value
of
f(x,
y)
=
x
+
y
over
the
region
in
 the
first
example
of
this
lesson.
 
 
 
 
 
 
 
 
 Do:

1.

Find
the
area
of
the
region
bounded
by
y
=
x,

y
=
6
–
x,
 and
x
=
0.
 
 
 2.

Find
the
average
value
of
f(x,
y)
=
x2y
over
this
region.
 
 
 
 
 
 ...
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