7-4 Arc Length

7-4 Arc Length
Example 1
Find the length of the arc of the semicubical parabola
>
between the points(1,1)and(4,8).
(1)
>
(2)
>
(3)
>
=
2
(4)
=
=
=
>
2
9
Example 2
Find the length of the arc of the semicubical parabola
>
from (0,0) to (1,1).
(5)
>
(6)
>
(7)
=
=
2
=
=
=
(7)
=
=
=
=
=
=
>
Example 3
(a)Set up an integral for the length of the arc of the hyperbola
from the point (1,1) to the point (2,
).
>
>
(8)
>
(9)
>
(10)
>
(b)Use Simpson's Rule with n=10 to estimate the arc length.
>
(11)
>
(12)
>
(13)
>
0.4531174003
Example 4
(14)
Find the arc length function for the curve
tacking P0(1,1) as starting point.
>
(15)
>
(16)
>
=
=
(17)
=
=
>
Find the length of the curve
3.
>
(18)
>
(19)
>
(20)
=
(20)
=
81
=
>
7.
>
(21)
>
(22)
>
(23)
=
=
=
2
2
(23)
=
=
=
=
>
9.
>
(24)
>
(25)
>
(26)
>
=
(27)
=
=
=
>
Use Simpson's Rule with n=10 to estimate the arc length of the curve.
Compare your answer with the value of the intergral produced by your calculator.
19.
>
>
(28)
>
(29)
>
(30)
(30)
>
0.2574893945
(31)
>
20.
>
>
(32)
>
(33)
>
0.8806418311
>
(34)