WEBVTT
1
00:00:00.440 --> 00:00:02.439 A:middle L:90%
she had square. So when you read here,
2
00:00:02.759 --> 00:00:07.389 A:middle L:90%
so we have our given, which is why is
3
00:00:07.400 --> 00:00:11.730 A:middle L:90%
equal to X to the 4/3. We have to
4
00:00:11.730 --> 00:00:15.699 A:middle L:90%
find the length of this curve between the 0.0 comma
5
00:00:15.699 --> 00:00:20.300 A:middle L:90%
zero and one common one. So we were gonna
6
00:00:20.300 --> 00:00:23.750 A:middle L:90%
integrate from 0 to 1 in respect to X.
7
00:00:24.440 --> 00:00:27.089 A:middle L:90%
But first we find the derivative, which gives us
8
00:00:27.089 --> 00:00:33.850 A:middle L:90%
4/3 thanks to the 1/3 power. So l is
9
00:00:33.850 --> 00:00:38.880 A:middle L:90%
equal to from 0 to 1 square root of one
10
00:00:38.880 --> 00:00:48.890 A:middle L:90%
plus four x to the 1/3 power over three square
11
00:00:49.539 --> 00:00:54.530 A:middle L:90%
D X. We're gonna substitute X. A sequel
12
00:00:54.530 --> 00:00:59.320 A:middle L:90%
to you. Cube gives us X. The X
13
00:00:59.329 --> 00:01:03.649 A:middle L:90%
is equal to three. You square. Do you
14
00:01:04.439 --> 00:01:10.180 A:middle L:90%
? Phil is equal to from 0 to 1 square
15
00:01:10.180 --> 00:01:18.719 A:middle L:90%
root of one plus for you cubed to the 1/3
16
00:01:18.719 --> 00:01:26.829 A:middle L:90%
power over three square time. Three you square,
17
00:01:27.030 --> 00:01:34.099 A:middle L:90%
do you? This becomes equal to integrate from 0
18
00:01:34.099 --> 00:01:41.030 A:middle L:90%
to 1 square bit of one plus for you over
19
00:01:41.030 --> 00:01:49.170 A:middle L:90%
three square times three years square, Do you?
20
00:01:51.540 --> 00:01:57.000 A:middle L:90%
This gives us from 0 to 1. You square
21
00:01:57.010 --> 00:02:06.540 A:middle L:90%
square root of nine plus 16 you square do you
22
00:02:07.439 --> 00:02:10.319 A:middle L:90%
so we're allowed to use the table of in took
23
00:02:10.319 --> 00:02:15.740 A:middle L:90%
roles. So I'm gonna use the into girl that
24
00:02:15.740 --> 00:02:23.889 A:middle L:90%
says integral You square he square plus you square do
25
00:02:23.889 --> 00:02:30.479 A:middle L:90%
you is equal to you Over eight times a square
26
00:02:31.240 --> 00:02:38.780 A:middle L:90%
close to you Square times square root of a square
27
00:02:38.780 --> 00:02:47.550 A:middle L:90%
Policy A square minus a to the fourth over Eat
28
00:02:49.539 --> 00:02:54.949 A:middle L:90%
Helen of you plus square root of a square Tewes
29
00:02:54.949 --> 00:03:01.080 A:middle L:90%
, you square plus c So we have this into
30
00:03:01.080 --> 00:03:07.919 A:middle L:90%
girl. This is equal to for from 0 to
31
00:03:07.919 --> 00:03:15.879 A:middle L:90%
1 you square square root of nine over 16 plus
32
00:03:15.879 --> 00:03:21.800 A:middle L:90%
you square, do you This is equal to four
33
00:03:23.039 --> 00:03:29.629 A:middle L:90%
Sarah one you square square root, uh, three
34
00:03:29.639 --> 00:03:39.569 A:middle L:90%
over four square plus u squared to you, which
35
00:03:39.569 --> 00:03:49.340 A:middle L:90%
is equal to four arms you over eight three over
36
00:03:49.340 --> 00:04:00.000 A:middle L:90%
four square plus two years square square root of three
37
00:04:00.009 --> 00:04:09.379 A:middle L:90%
over four square plus you square minus one over eight
38
00:04:10.620 --> 00:04:16.850 A:middle L:90%
homes three over four The fourth power I'll end of
39
00:04:16.850 --> 00:04:26.730 A:middle L:90%
you plus square root A three over four square plus
40
00:04:26.730 --> 00:04:31.810 A:middle L:90%
you square and we integrate this from 0 to 1
41
00:04:36.680 --> 00:04:44.250 A:middle L:90%
. This is equal to four times you over eight
42
00:04:46.240 --> 00:04:57.709 A:middle L:90%
34 square plus two you square comes the square root
43
00:04:57.720 --> 00:05:08.189 A:middle L:90%
of 34 square plus you square minus one over eight
44
00:05:09.139 --> 00:05:15.949 A:middle L:90%
tons. 3/4 over four l and of you plus
45
00:05:15.949 --> 00:05:25.040 A:middle L:90%
square root of three over four square. Plus he
46
00:05:25.040 --> 00:05:30.649 A:middle L:90%
is square. We integrate this from 0 to 1
47
00:05:30.910 --> 00:05:42.350 A:middle L:90%
and it gives us 205 over 128 minus 81 Ln
48
00:05:42.350 --> 00:05:46.649 A:middle L:90%
of three over 512.