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CHAPTER 29
Fig. 29-6
Fig. 29-7
29.30
29.31
29.32
29.33
29.34
29.35
29.36
Find the arc length of the parabola
As x increases from 0 to 2, increases from 0 to a = tan 4 (Fig. 29-7). So, by
Problem 28.40 :
Find the arc length of the curve y = lnx from (1,0) to (e, 1).
Then, using Problem 29.21,
Find the arc length of the curve y = e" from (0,1) to (1, e).
This has the same answer as Problem 29.31, since the two arcs are mirror images of each other in the line
Find the arc length of the curve y = In cos x from (0, 0) to (ir/3, —In 2).
Find
From the identity
we obtain
Thus
Hence,
From the identity
Find J(l+cosfljc)
3/2 d;c.
we get
From the identity in the solution of Problem 29.34,
Find
Hence,
l + (/)
2 = sec
2 ;t.
So
L = J 0 "
3 sec x dx = In |sec x + tan x\ ]%'
3 =
y' = 2x. So L =
y = x
2
from (0,0) to (2,4).
Let x = 5 tan 0, dx = \ sec" 6 d6,
sec
3 6 dd = \(l&n 0 sec 0 + In |sec 6 + tan 0|) ]o =
In
In