WEBVTT
1
00:00:00.440 --> 00:00:02.859 A:middle L:90%
we know that we're using the disk and washing method
2
00:00:02.859 --> 00:00:05.530 A:middle L:90%
to integrate along the access parallel to the axis of
3
00:00:05.530 --> 00:00:09.630 A:middle L:90%
rotation. So the outer radius is gonna be one
4
00:00:09.630 --> 00:00:12.070 A:middle L:90%
minus year, which is one cause the distance from
5
00:00:12.070 --> 00:00:14.070 A:middle L:90%
Y equals one of the axis of rotation, which
6
00:00:14.070 --> 00:00:16.429 A:middle L:90%
is why I call zero. And the inner radius
7
00:00:16.440 --> 00:00:19.109 A:middle L:90%
is gonna be the 432 acts again for the same
8
00:00:19.109 --> 00:00:22.260 A:middle L:90%
reasons. Distance to the axis of rotation. Therefore
9
00:00:22.260 --> 00:00:25.449 A:middle L:90%
, our volume is pi times the integral from 01
10
00:00:26.640 --> 00:00:30.429 A:middle L:90%
outer, which is ones, and it's squared minus
11
00:00:30.440 --> 00:00:40.670 A:middle L:90%
inner 432 ax squared D X integrate, which means
12
00:00:40.670 --> 00:00:43.689 A:middle L:90%
use the power rule. Increase the experiment by wand
13
00:00:44.070 --> 00:00:50.280 A:middle L:90%
and divide by the new exponents. And now we
14
00:00:50.280 --> 00:00:52.670 A:middle L:90%
can plug in our values zero and one or two
15
00:00:52.670 --> 00:01:02.659 A:middle L:90%
bounds. As you can see, we end up
16
00:01:02.659 --> 00:01:03.549 A:middle L:90%
with pi over three