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| PAGE: 568 | SET: Exercises | PROBLEM: 28 |
The curve is 
on interval 
.
(a)
Graph the curve 
on interval 
.
Graph:
.
(b)
The curve is .
The polygon with one side 
is the line segment between 
and 
.
Consider 
.
Substitute 
in 
.
.
The one end point of the line segment is 
.
Substitute 
in .
The other end point of the line segment is 
.
The length of curve is 
.
The polygon with two sides 
join the line segments between , 
and 
.
Substitute 
in .
.
The one end point on the line segment is 
.
The length of the curve is is 
.
The polygon with four sides 
join the line segments between , 
, 
, 
and .
Substitute 
in .
The point is 
.
Substitute 
in .
The point is 
.
The arc length is 
.
(c)
The curve is and the interval is .
Length of the curve 
on the interval 
is 
.
Find 
.
Apply derivative on each side with respect to 
.
.
The length of the curve is 
.
(d)
Length of the curve is 
.
Using calculator the value of 
.
The length of the curve is approximately 
is larger than other approximations.
The length of the curve using polygons with sides 
are small when compared to 
.
(a) Graph of the curve on interval .
.
(b) 
, 
and 
.
(c) Length of the curve is .
(d) The length of the curve using polygons with sides 
are small when compared to .
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