WEBVTT
1
00:00:00.640 --> 00:00:02.470 A:middle L:90%
he is clear. So when you read here,
2
00:00:02.470 --> 00:00:08.119 A:middle L:90%
so we have f of acts is equal to inverse
3
00:00:08.369 --> 00:00:13.810 A:middle L:90%
sine plus square root of one minus x square.
4
00:00:16.379 --> 00:00:23.850 A:middle L:90%
So we take the derivative When we got one over
5
00:00:24.339 --> 00:00:32.590 A:middle L:90%
square of one minus X square minus two x over
6
00:00:32.590 --> 00:00:36.750 A:middle L:90%
to times square root of one minus x square.
7
00:00:38.579 --> 00:00:43.929 A:middle L:90%
This becomes equal to one minus X over a square
8
00:00:43.939 --> 00:00:48.939 A:middle L:90%
of one minus X square, which is equal to
9
00:00:48.939 --> 00:00:54.850 A:middle L:90%
square root of one minus X over one plus nuts
10
00:00:57.380 --> 00:01:00.359 A:middle L:90%
. So in our arguing formula, we know that
11
00:01:00.369 --> 00:01:03.049 A:middle L:90%
there is the square root of one plus F,
12
00:01:04.040 --> 00:01:12.129 A:middle L:90%
the derivative of F square. So one points here
13
00:01:12.129 --> 00:01:23.620 A:middle L:90%
, I'll write it. This becomes equal to the
14
00:01:23.620 --> 00:01:30.939 A:middle L:90%
square root of two over one plus X, which
15
00:01:30.939 --> 00:01:34.959 A:middle L:90%
is equal to we just square with them individually.
16
00:01:41.040 --> 00:01:42.650 A:middle L:90%
So we just have to plug it into our Klink
17
00:01:44.319 --> 00:01:51.799 A:middle L:90%
function. So from zero to x square, Burt
18
00:01:51.810 --> 00:01:57.250 A:middle L:90%
of two over square root of one plus t 18
19
00:01:59.739 --> 00:02:02.450 A:middle L:90%
we're gonna make you be equal to one plus t
20
00:02:04.939 --> 00:02:08.050 A:middle L:90%
. So d t is equal to do you.
21
00:02:09.639 --> 00:02:15.969 A:middle L:90%
This changes our limits of integration too. One one
22
00:02:15.969 --> 00:02:21.259 A:middle L:90%
plus x. We're just adding one when we get
23
00:02:22.240 --> 00:02:38.069 A:middle L:90%
square root of two integration 11 plus X one over
24
00:02:38.069 --> 00:02:45.389 A:middle L:90%
square root of you, Do you? This becomes
25
00:02:45.389 --> 00:02:52.340 A:middle L:90%
equal to square it of you to you to the
26
00:02:52.340 --> 00:02:59.500 A:middle L:90%
1/2 power from 1 to 1 plus acts, miss
27
00:02:59.509 --> 00:03:04.840 A:middle L:90%
equals two square root of two runs a swear it
28
00:03:04.849 --> 00:03:08.219 A:middle L:90%
of one plus x minus one