WEBVTT
1
00:00:00.140 --> 00:00:02.879 A:middle L:90%
So we're doing the integral from 0 to 1 of
2
00:00:02.879 --> 00:00:08.339 A:middle L:90%
this function. And pointing out the product here um
3
00:00:08.349 --> 00:00:13.359 A:middle L:90%
because we don't have a product rule for anti derivatives
4
00:00:13.839 --> 00:00:17.589 A:middle L:90%
and instead of writing the cuBA and the 1/4 root
5
00:00:17.589 --> 00:00:19.539 A:middle L:90%
, I'm writing what's equivalent to that, which is
6
00:00:19.539 --> 00:00:21.620 A:middle L:90%
to the one third powers of cuba at the 1/4
7
00:00:21.620 --> 00:00:26.059 A:middle L:90%
powers is four through. Um And what I would
8
00:00:26.059 --> 00:00:28.070 A:middle L:90%
have my sense to is distribute this in. So
9
00:00:28.070 --> 00:00:32.240 A:middle L:90%
now it is uh polynomial. And just remember that
10
00:00:32.240 --> 00:00:34.340 A:middle L:90%
when you're multiplying with the same base, you add
11
00:00:34.340 --> 00:00:38.119 A:middle L:90%
the exponents before thirds And then this would be to
12
00:00:38.119 --> 00:00:42.299 A:middle L:90%
the five force power. So now we're ready to
13
00:00:42.299 --> 00:00:45.530 A:middle L:90%
do the anti directive which is adding one to the
14
00:00:45.530 --> 00:00:48.200 A:middle L:90%
exponent. It might make sense to write it as
15
00:00:48.210 --> 00:00:50.490 A:middle L:90%
three thirds to help you add one, I don't
16
00:00:50.490 --> 00:00:51.759 A:middle L:90%
know, I just assumed you knew how to do
17
00:00:51.759 --> 00:00:56.149 A:middle L:90%
that before and then multiply by the reciprocal. So
18
00:00:56.149 --> 00:00:58.899 A:middle L:90%
this one you're adding four force, which is exactly
19
00:00:58.899 --> 00:01:00.850 A:middle L:90%
what it did over here. So it's really the
20
00:01:00.850 --> 00:01:03.450 A:middle L:90%
same math. But then multiply by the reciprocal.
21
00:01:04.239 --> 00:01:07.060 A:middle L:90%
I should be putting equals in here by the way
22
00:01:07.540 --> 00:01:08.250 A:middle L:90%
. Um and we're going from 0-1. So it's
23
00:01:08.250 --> 00:01:11.409 A:middle L:90%
really nice about this. Problem is when you plug
24
00:01:11.409 --> 00:01:15.189 A:middle L:90%
in the upper bound and for your exes well one
25
00:01:15.189 --> 00:01:15.840 A:middle L:90%
to any power is just one. Think of the
26
00:01:15.840 --> 00:01:18.780 A:middle L:90%
cube root of one is one to the seventh hour
27
00:01:18.780 --> 00:01:22.170 A:middle L:90%
still one. So we're just looking at 3/7 plus
28
00:01:22.170 --> 00:01:26.560 A:middle L:90%
4/9. And then you'll be subtracting off. And
29
00:01:26.560 --> 00:01:29.450 A:middle L:90%
I still encourage all my students to put in zeros
30
00:01:29.459 --> 00:01:30.930 A:middle L:90%
in there. Just because when you do like co
31
00:01:30.930 --> 00:01:34.030 A:middle L:90%
sign of zero or either the zero power, you
32
00:01:34.030 --> 00:01:37.569 A:middle L:90%
actually get numerical value. So this case you do
33
00:01:37.569 --> 00:01:40.560 A:middle L:90%
not get anything subtracting zero is not going to change
34
00:01:41.040 --> 00:01:42.849 A:middle L:90%
. So I would get the same denominator in these
35
00:01:42.849 --> 00:01:45.349 A:middle L:90%
two. And what I would have to do is
36
00:01:45.349 --> 00:01:49.430 A:middle L:90%
multiply this piece by 9/9 to get that denominator of
37
00:01:49.430 --> 00:01:52.430 A:middle L:90%
63. So we're looking at 27. And over
38
00:01:52.430 --> 00:01:56.549 A:middle L:90%
here I'd have to multiply by 7/7s To get 28
39
00:01:57.640 --> 00:02:01.019 A:middle L:90%
. Um as that X numerator, Uh when you
40
00:02:01.019 --> 00:02:06.260 A:middle L:90%
add those, you get the correct answer of 55/63
41
00:02:07.239 --> 00:02:07.349 A:middle L:90%
. There you go.