Section 6.1:
Areas Between Curves
If use ‘vertical’ rectangles whose base has a width of
∆
x
:
The area
A
of the region bounded by the curves
y
=
f x
( 29
,
y
=
g x
( 29
, and
the lines
x
=
a
,
x
=
b
, where
f
and
g
are continuous and
f x
( 29
≥
g x
( 29
for
a
≤
x
≤
b
is
A
=
f x
( 29 
g x
( 29
[
]
dx
a
b
∫
.
The integrand should be expressed as upper curve minus lower curve.
If use ‘horizontal’ rectangles whose base has a width of
∆
y
:
The area a of the region bounded by the curves
x
=
f y
( 29
,
x
=
g y
( 29
, and
the lines
y
=
c
,
y
=
d
, where f and g are continuous and
f y
( 29
≥
g y
( 29
for
c
≤
y
≤
d
is
A
=
f y
( 29

g y
( 29
[
]
dy
c
d
∫
.
The integrand should be expressed as rightmost curve minus leftmost
curve.
Example.
Determine the area bounded by the curves
y
=
x
2
and
y
=
x
both ways.
In
other words, using ‘vertical’ rectangles and then using ‘horizontal’ rectangles.
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This note was uploaded on 01/12/2010 for the course MATH 44245 taught by Professor Famiglietti during the Fall '07 term at UC Irvine.
 Fall '07
 FAMIGLIETTI
 Math, Angles

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