The length of the arc of the curve x-f(t), y π(t)
included between two points whose parametric values are alpha, beta is
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the previous two sections we’ve looked at a couple of Calculus I topics in terms of parametric equations. We now need to look at a couple of Calculus II topics in terms of parametric equations.
In this section we will look at the arc length of the parametric curve given by,
x
=
f
(
t
)
y
=
g
(
t
)
α
≤
t
≤
β
We will also be assuming that the curve is traced out exactly once as
t
increases from
α
to
β
. We will also need to assume that the curve is traced out from left to right as
t
increases. This is equivalent to saying,
d
x
d
t
≥
0
for
α
≤
t
≤
β
So, let’s start out the derivation by recalling the arc length formula as we first derived it in the arc length section of the Applications of Integrals chapter.
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