Question

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
​

Answer 1

Answer:

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.