WEBVTT
1
00:00:01.540 --> 00:00:04.459 A:middle L:90%
the functions F N g r as shown. We
2
00:00:04.459 --> 00:00:06.570 A:middle L:90%
want to determine what is the total area between the
3
00:00:06.570 --> 00:00:10.500 A:middle L:90%
curves for his exit between zero and five. So
4
00:00:10.500 --> 00:00:13.099 A:middle L:90%
we know that this first region has an area of
5
00:00:13.099 --> 00:00:15.849 A:middle L:90%
12 and the second region has an area of 27
6
00:00:16.269 --> 00:00:19.809 A:middle L:90%
. So the total area total area is equal to
7
00:00:20.239 --> 00:00:25.359 A:middle L:90%
12 plus 27 which is equal to 39. Next
8
00:00:25.359 --> 00:00:27.640 A:middle L:90%
, we want to determine the value of the integral
9
00:00:27.649 --> 00:00:30.120 A:middle L:90%
of F minus g. So we see that in
10
00:00:30.120 --> 00:00:33.250 A:middle L:90%
the first region F is below Gee So that means
11
00:00:33.250 --> 00:00:39.390 A:middle L:90%
that this actually will be considered as a negative in
12
00:00:39.390 --> 00:00:42.049 A:middle L:90%
the integral. And this area over here will be
13
00:00:42.049 --> 00:00:45.270 A:middle L:90%
considered positive since F is greater than G. So
14
00:00:45.270 --> 00:00:49.590 A:middle L:90%
the value of this integral is equal to here.
15
00:00:49.590 --> 00:00:55.609 A:middle L:90%
We have a negative 12 plus a 27 which is
16
00:00:55.619 --> 00:00:57.649 A:middle L:90%
equal to 15