WEBVTT
1
00:00:00.540 --> 00:00:06.790 A:middle L:90%
the problem is find the area of the region only
2
00:00:06.799 --> 00:00:10.839 A:middle L:90%
by the given curves here. Why is they go
3
00:00:10.839 --> 00:00:14.599 A:middle L:90%
to High Square l N X and why is they
4
00:00:14.599 --> 00:00:19.440 A:middle L:90%
go to four times l n X? First we
5
00:00:19.440 --> 00:00:25.239 A:middle L:90%
lied. These two functions uh, echo and find
6
00:00:25.250 --> 00:00:30.420 A:middle L:90%
intersection Point. Let's say this is X choir minus
7
00:00:30.429 --> 00:00:36.609 A:middle L:90%
or times Helen likes is equal to zero. This
8
00:00:36.619 --> 00:00:42.869 A:middle L:90%
X is greater than zero. We have X is
9
00:00:42.880 --> 00:00:46.770 A:middle L:90%
equal to tool or Alan. Tax is 0 to
10
00:00:46.780 --> 00:00:55.600 A:middle L:90%
0. So this actually why Mhm So the interval
11
00:00:55.600 --> 00:01:02.350 A:middle L:90%
is from 1 to 2 and what acts is between
12
00:01:02.359 --> 00:01:07.219 A:middle L:90%
one and two. Four times L and X is
13
00:01:07.219 --> 00:01:12.549 A:middle L:90%
great as on I squared times our next since I
14
00:01:12.549 --> 00:01:19.269 A:middle L:90%
rear bounded by given curves is integral from 1 to
15
00:01:19.269 --> 00:01:23.959 A:middle L:90%
2 or times are impacts minus X choir times out
16
00:01:23.969 --> 00:01:29.829 A:middle L:90%
next thanks, or this is equal to the integral
17
00:01:29.829 --> 00:01:34.920 A:middle L:90%
from 1 to 2 four minus X choir. Alan
18
00:01:34.920 --> 00:01:42.239 A:middle L:90%
Nex Next. Now we can use integration by parts
19
00:01:42.239 --> 00:01:47.299 A:middle L:90%
to southeast. Integral former is integral of U K
20
00:01:47.299 --> 00:01:53.269 A:middle L:90%
. Prime Detox is legal to you'll be minus the
21
00:01:53.280 --> 00:01:57.159 A:middle L:90%
integral of your prime rejects. Now we can let
22
00:01:57.170 --> 00:02:02.159 A:middle L:90%
you is the co two warm minus X choir.
23
00:02:02.170 --> 00:02:09.159 A:middle L:90%
And we now when u is equal to Highland Max
24
00:02:09.840 --> 00:02:15.650 A:middle L:90%
and we promise to four minus x squared, then
25
00:02:15.039 --> 00:02:21.120 A:middle L:90%
well, you promise people wanna racks V a secretary
26
00:02:22.439 --> 00:02:28.949 A:middle L:90%
or acts minus what third tax to three is power
27
00:02:30.740 --> 00:02:36.129 A:middle L:90%
, then this integral. It's a cultural new times
28
00:02:36.129 --> 00:02:42.289 A:middle L:90%
we So this is or X minus one third x
29
00:02:42.289 --> 00:02:47.569 A:middle L:90%
two threes power times l and X from 12 to
30
00:02:47.580 --> 00:02:53.620 A:middle L:90%
minus interior from 1 to 2. You prime time
31
00:02:53.620 --> 00:02:57.860 A:middle L:90%
, sweetie. So this is more minus my dude
32
00:02:58.240 --> 00:03:04.060 A:middle L:90%
X square. Mm x such as is you,
33
00:03:04.060 --> 00:03:07.680 A:middle L:90%
can't you? So for the first term, we
34
00:03:07.680 --> 00:03:10.460 A:middle L:90%
plug in two and 12 blocks than behalf. This
35
00:03:10.460 --> 00:03:17.870 A:middle L:90%
is eight minus it over. Three times Ellen Chew
36
00:03:17.919 --> 00:03:24.490 A:middle L:90%
and minus zero and minus. And to grow this
37
00:03:24.490 --> 00:03:30.319 A:middle L:90%
oneness war axe minus one. Number nine x two
38
00:03:30.330 --> 00:03:36.759 A:middle L:90%
threes. Power from one to this is true.
39
00:03:38.340 --> 00:03:46.590 A:middle L:90%
16/3 hour in two minus This one who is eight
40
00:03:46.680 --> 00:03:54.659 A:middle L:90%
minus 8/9 minus four, minus one over I.
41
00:04:01.139 --> 00:04:06.259 A:middle L:90%
So this is the result