WEBVTT
1
00:00:00.640 --> 00:00:03.950 A:middle L:90%
here we have the integral of one over co sign
2
00:00:03.950 --> 00:00:09.349 A:middle L:90%
of X minus one. One way to proceed here
3
00:00:09.740 --> 00:00:13.710 A:middle L:90%
is to multiply. That happened the bottom by one
4
00:00:13.710 --> 00:00:34.640 A:middle L:90%
plus co sign X. So, after doing so
5
00:00:34.640 --> 00:00:42.679 A:middle L:90%
, let's go ahead and multiply out the denominator with
6
00:00:42.689 --> 00:00:46.609 A:middle L:90%
co sign X plus one in the numerator and in
7
00:00:46.609 --> 00:00:52.549 A:middle L:90%
the denominator, we have cosign squared X minus one
8
00:00:57.590 --> 00:01:00.280 A:middle L:90%
. So using the Pythagorean identity, we can rewrite
9
00:01:00.280 --> 00:01:22.500 A:middle L:90%
this denominator as negative science. Where and then let's
10
00:01:22.500 --> 00:01:25.670 A:middle L:90%
go ahead and split up this into grand into two
11
00:01:25.670 --> 00:01:33.959 A:middle L:90%
fractions. We have coastline, eggs, overnegative,
12
00:01:33.959 --> 00:01:47.549 A:middle L:90%
sign square plus one over negative science where using our
13
00:01:47.549 --> 00:01:49.540 A:middle L:90%
knowledge of trigonometry, we could go ahead and re
14
00:01:49.540 --> 00:01:55.049 A:middle L:90%
write these. So for the first in our group
15
00:01:55.049 --> 00:02:00.260 A:middle L:90%
, we have negative Cho attention of X time's cozy
16
00:02:00.260 --> 00:02:14.615 A:middle L:90%
Kennebec and for the second integral, we have negative
17
00:02:14.944 --> 00:02:16.534 A:middle L:90%
Kosi can square of x, d, d x
18
00:02:17.794 --> 00:02:22.185 A:middle L:90%
and we we know from our table or from previous
19
00:02:22.185 --> 00:02:27.064 A:middle L:90%
examples that evaluate each of these two. So this
20
00:02:27.064 --> 00:02:31.935 A:middle L:90%
is cozy convicts and the integral of negative Kosi can
21
00:02:31.935 --> 00:02:38.604 A:middle L:90%
squared is coast engine of X, plus our constancy
22
00:02:38.694 --> 00:02:39.604 A:middle L:90%
. And that's our answer