WEBVTT
1
00:00:00.340 --> 00:00:05.919 A:middle L:90%
so the volume is generated. Volume generated is given
2
00:00:05.919 --> 00:00:11.650 A:middle L:90%
by the Formula A B uh, you know,
3
00:00:12.390 --> 00:00:17.410 A:middle L:90%
every squared of X minus G sweat of X and
4
00:00:17.410 --> 00:00:21.050 A:middle L:90%
then DX. Right. Okay. So, um
5
00:00:23.210 --> 00:00:25.879 A:middle L:90%
, you know, that is just gonna be pi
6
00:00:26.230 --> 00:00:28.899 A:middle L:90%
. What is the no limit is one upper limit
7
00:00:28.899 --> 00:00:34.600 A:middle L:90%
is to use who and then f is given as
8
00:00:35.079 --> 00:00:37.280 A:middle L:90%
one over X one. It was great. Deal
9
00:00:37.280 --> 00:00:41.840 A:middle L:90%
of experience. Three one of the square root off
10
00:00:41.850 --> 00:00:46.719 A:middle L:90%
eggs into three minus x. Okay, So the
11
00:00:46.719 --> 00:00:48.829 A:middle L:90%
squared here means that a square root is gonna go
12
00:00:48.829 --> 00:00:52.310 A:middle L:90%
away. So she's gonna be won over one of
13
00:00:52.310 --> 00:00:58.960 A:middle L:90%
her ex three minus X. Okay. And then
14
00:00:59.439 --> 00:01:07.379 A:middle L:90%
this is Oh, zero. Right. So did
15
00:01:07.379 --> 00:01:08.090 A:middle L:90%
you have X parties? Hero? So you just
16
00:01:08.090 --> 00:01:12.700 A:middle L:90%
have the X right here. Okay. So what
17
00:01:12.700 --> 00:01:15.750 A:middle L:90%
is the integral off? This guy right here?
18
00:01:17.519 --> 00:01:19.900 A:middle L:90%
I'm gonna use partial fractions once again. Right,
19
00:01:19.909 --> 00:01:23.280 A:middle L:90%
Because the rational function, one of the ways to
20
00:01:23.280 --> 00:01:26.650 A:middle L:90%
go about it is partial fraction. So we're just
21
00:01:26.650 --> 00:01:29.890 A:middle L:90%
gonna take the rational function and make it a over
22
00:01:29.890 --> 00:01:34.890 A:middle L:90%
the 1st 1 then plus B over a 2nd 1
23
00:01:34.900 --> 00:01:38.719 A:middle L:90%
right? And then we can I just do the
24
00:01:38.719 --> 00:01:44.239 A:middle L:90%
LCD and then group equate the new Raiders right with
25
00:01:44.239 --> 00:01:47.290 A:middle L:90%
doing this many times, You gonna let X equal
26
00:01:47.290 --> 00:01:49.250 A:middle L:90%
zero when X equals zero, Then we just have
27
00:01:49.250 --> 00:01:56.769 A:middle L:90%
38 Right? And then a is 1/3 and over
28
00:01:56.780 --> 00:01:59.620 A:middle L:90%
. Let X equals one. And what is happening
29
00:02:00.090 --> 00:02:02.819 A:middle L:90%
then? X equals three because we will eliminate a
30
00:02:04.150 --> 00:02:05.950 A:middle L:90%
So when X equals three, you can see that
31
00:02:05.950 --> 00:02:07.680 A:middle L:90%
this one is gonna be zero. So Ace eliminated
32
00:02:08.199 --> 00:02:12.449 A:middle L:90%
. So this is gonna be three b, right
33
00:02:12.460 --> 00:02:15.949 A:middle L:90%
? And therefore me is also one of three.
34
00:02:15.439 --> 00:02:22.750 A:middle L:90%
So this interval right here becomes high. 12 Okay
35
00:02:23.789 --> 00:02:30.240 A:middle L:90%
, uh, 1/3, X plus 1/3, three
36
00:02:30.240 --> 00:02:34.689 A:middle L:90%
minus six. Right. So once you have this
37
00:02:34.689 --> 00:02:37.129 A:middle L:90%
one, then the integral and do it in a
38
00:02:37.139 --> 00:02:43.599 A:middle L:90%
different color, and the integral becomes I. This
39
00:02:43.599 --> 00:02:49.539 A:middle L:90%
one becomes 1/3 natural Law X. And then this
40
00:02:49.539 --> 00:02:55.889 A:middle L:90%
one becomes negative. 1/3. Not to look three
41
00:02:55.889 --> 00:03:00.550 A:middle L:90%
minus x. And then we put one and two
42
00:03:00.550 --> 00:03:04.310 A:middle L:90%
here. Right? So when you do our parliament
43
00:03:04.310 --> 00:03:07.729 A:middle L:90%
minus lower limits, right? What do you have
44
00:03:07.879 --> 00:03:14.889 A:middle L:90%
? You have I over three, right, Natural
45
00:03:14.889 --> 00:03:20.419 A:middle L:90%
lago four. And since it's a volume that its
46
00:03:20.419 --> 00:03:23.560 A:middle L:90%
units cute rice or the volume is given by this
47
00:03:23.439 --> 00:03:24.860 A:middle L:90%
right here. Right can do. A lot of
48
00:03:24.860 --> 00:03:27.189 A:middle L:90%
the women is the one of me. Just put
49
00:03:27.189 --> 00:03:30.139 A:middle L:90%
two on every C X and that minus you Put
50
00:03:30.150 --> 00:03:31.520 A:middle L:90%
one. Whenever you see X, you arrive with
51
00:03:31.520 --> 00:03:34.819 A:middle L:90%
this answer. Right. So this is the volume
52
00:03:34.819 --> 00:03:38.150 A:middle L:90%
of the volume generated, Okay.