WEBVTT
1
00:00:00.140 --> 00:00:02.910 A:middle L:90%
So here we give an example of a certain integral
2
00:00:03.339 --> 00:00:05.559 A:middle L:90%
, you have the integral from 0 to 2 of
3
00:00:05.570 --> 00:00:08.630 A:middle L:90%
two. Y minus y squared, do we?
4
00:00:08.630 --> 00:00:11.630 A:middle L:90%
So we'll just solve this integral to the integral of
5
00:00:11.640 --> 00:00:14.720 A:middle L:90%
two. Y is just y squared. And the
6
00:00:14.720 --> 00:00:17.050 A:middle L:90%
integral of y squared would be Y to the n
7
00:00:17.050 --> 00:00:19.289 A:middle L:90%
plus one over n plus one. So if you're
8
00:00:19.289 --> 00:00:23.679 A:middle L:90%
y cube over three and this integral goes from 0
9
00:00:23.690 --> 00:00:28.350 A:middle L:90%
to zero, makes no contribution. Here, Tattoo
10
00:00:28.350 --> 00:00:34.429 A:middle L:90%
squared would be four minus eight thirds, so four
11
00:00:34.429 --> 00:00:38.149 A:middle L:90%
is 12 3rd, so this becomes equal to 12
12
00:00:38.149 --> 00:00:42.570 A:middle L:90%
, 3rd times 8/3 is 4/3. This will be
13
00:00:42.570 --> 00:00:48.840 A:middle L:90%
4/3 units squared. So we also can draw a
14
00:00:48.840 --> 00:00:53.130 A:middle L:90%
diagram of this. So when we have a problem
15
00:00:53.130 --> 00:00:59.530 A:middle L:90%
of the form of Y times two minus why the
16
00:00:59.539 --> 00:01:03.560 A:middle L:90%
X is essentially equivalent to zero when y equals zero
17
00:01:04.040 --> 00:01:12.439 A:middle L:90%
And when y equals two. And also since the
18
00:01:12.439 --> 00:01:17.629 A:middle L:90%
contribution is minus y squared, the problem is going
19
00:01:17.629 --> 00:01:21.310 A:middle L:90%
to be open to the left. In this case
20
00:01:23.739 --> 00:01:26.409 A:middle L:90%
. As a result, we have some form of
21
00:01:26.409 --> 00:01:29.379 A:middle L:90%
a problem like this. And Manly were interested in
22
00:01:29.379 --> 00:01:32.950 A:middle L:90%
finding the area of this region and this gives our
23
00:01:32.959 --> 00:01:33.659 A:middle L:90%
final answer