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13.3 Arc Length and Curvature
There are several approaches to finding the length of a portion of the graph of a function.
In section 8.1 arc length is found using integrals and derivatives.
From 8.1 (page 542),
If
'
f
is continuous on [a,b], then the length of the curve
is
()
,,
yfxaxb
=≤
≤
2
1'
b
a
Lf
x
=+
∫
d
x
β
≤
In section 10.3, a formula for arc length is given for the parametric equations
, but there are some restrictions (see page 656).
,
,
xf
tyg
t
t
α
== ≤
22
dx
dy
Ld
dt
dt
∫
t
Arc length can also be found for a polar curve,
2
2
b
a
dr
Lr
d
θ
∫
d
(see page 673 for
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 Fall '08
 Estrada
 Arc Length, Derivative, Integrals

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