WEBVTT
1
00:00:02.339 --> 00:00:05.669 A:middle L:90%
All right, we are going to answer the question
2
00:00:06.040 --> 00:00:09.089 A:middle L:90%
. What is the value of one integration from 1
3
00:00:09.089 --> 00:00:12.800 A:middle L:90%
to 1? The square root of one plus X
4
00:00:12.800 --> 00:00:17.250 A:middle L:90%
to the fourth the X. Okay, I already
5
00:00:17.250 --> 00:00:19.910 A:middle L:90%
know the answer. It only takes half a second
6
00:00:19.910 --> 00:00:22.969 A:middle L:90%
to solve this thing. But why can I do
7
00:00:22.969 --> 00:00:26.469 A:middle L:90%
that? It's actually based on this idea. The
8
00:00:26.480 --> 00:00:33.539 A:middle L:90%
area between the curve and the X axis is written
9
00:00:33.539 --> 00:00:37.850 A:middle L:90%
like this. Okay, so one of the first
10
00:00:37.850 --> 00:00:41.619 A:middle L:90%
properties that you can see right away is that if
11
00:00:41.619 --> 00:00:44.549 A:middle L:90%
the area under the curve it's on Lee from a
12
00:00:44.549 --> 00:00:48.289 A:middle L:90%
T A f m x dx, it really doesn't
13
00:00:48.289 --> 00:00:51.630 A:middle L:90%
matter what f of X is equal to. So
14
00:00:51.630 --> 00:00:55.659 A:middle L:90%
if I try to grow, graph it. Let's
15
00:00:55.659 --> 00:00:58.240 A:middle L:90%
say that I have a drawing like this. I
16
00:00:58.240 --> 00:01:03.359 A:middle L:90%
started a and I end at a So what's the
17
00:01:03.369 --> 00:01:07.959 A:middle L:90%
area under the curve off the line that has,
18
00:01:07.540 --> 00:01:11.609 A:middle L:90%
with of zero. Well, I don't know what
19
00:01:11.609 --> 00:01:14.650 A:middle L:90%
the height is going to be. I meant I
20
00:01:14.650 --> 00:01:18.939 A:middle L:90%
don't know what the function is going to be,
21
00:01:18.939 --> 00:01:21.930 A:middle L:90%
but ffx is gonna have ah, height f of
22
00:01:21.939 --> 00:01:25.159 A:middle L:90%
A and Delta X is equal to zero. So
23
00:01:25.159 --> 00:01:27.530 A:middle L:90%
the area it's just zero because it's f of eight
24
00:01:27.530 --> 00:01:30.180 A:middle L:90%
times zero. Okay, So what is this equal
25
00:01:30.180 --> 00:01:36.060 A:middle L:90%
to zero? What is this equal to? Well
26
00:01:36.540 --> 00:01:38.689 A:middle L:90%
, from 1 to 1, the area under the
27
00:01:38.689 --> 00:01:42.129 A:middle L:90%
curve, regardless of what this guy is, has
28
00:01:42.129 --> 00:01:47.040 A:middle L:90%
to be zero. And that's how you answer this
29
00:01:47.040 --> A:middle L:90%
question.