WEBVTT
1
00:00:00.800 --> 00:00:05.559 A:middle L:90%
Let's go ahead and evaluate the integral, starting with
2
00:00:05.559 --> 00:00:08.849 A:middle L:90%
the left hand side. Let's just go ahead and
3
00:00:10.240 --> 00:00:29.059 A:middle L:90%
distribute this. So let's expand this numerator and then
4
00:00:29.070 --> 00:00:33.700 A:middle L:90%
denominators stays the same. So all we did there
5
00:00:33.700 --> 00:00:38.299 A:middle L:90%
was expand. Now let's go ahead and simplify this
6
00:00:38.840 --> 00:00:41.149 A:middle L:90%
. So this we should go ahead and do long
7
00:00:41.149 --> 00:00:44.649 A:middle L:90%
division here. So let's go to the side.
8
00:00:45.140 --> 00:00:49.329 A:middle L:90%
Do that. We've done this before. Can't a
9
00:00:49.329 --> 00:00:52.750 A:middle L:90%
synthetic Yuri will need long division because of the quadratic
10
00:00:53.340 --> 00:00:57.350 A:middle L:90%
. But after you do your long division over,
11
00:01:00.539 --> 00:01:03.899 A:middle L:90%
So I'm making no here long division or polynomial division
12
00:01:03.899 --> 00:01:14.900 A:middle L:90%
, I should say five x of the forth.
13
00:01:14.900 --> 00:01:19.019 A:middle L:90%
So this is the quotient, and then you get
14
00:01:19.019 --> 00:01:25.030 A:middle L:90%
a remainder of minus four and then the original denominator
15
00:01:25.040 --> 00:01:27.400 A:middle L:90%
. So this becomes the general. As you see
16
00:01:27.400 --> 00:01:30.140 A:middle L:90%
, we can just use upon rule whole bunch of
17
00:01:30.140 --> 00:01:33.140 A:middle L:90%
times and then the very last one here, you
18
00:01:33.140 --> 00:01:38.010 A:middle L:90%
write. Remember this. You hear? This will
19
00:01:38.010 --> 00:01:41.799 A:middle L:90%
just be fourteen in verse. But if you feel
20
00:01:41.799 --> 00:01:44.400 A:middle L:90%
about that fact, you can go ahead and just
21
00:01:44.400 --> 00:01:47.739 A:middle L:90%
do it. Trips up here, That's equals tan
22
00:01:47.739 --> 00:01:53.180 A:middle L:90%
data. So when we evaluate this exit, the
23
00:01:53.180 --> 00:02:00.349 A:middle L:90%
seven over seven for exit the six over six find
24
00:02:00.349 --> 00:02:06.969 A:middle L:90%
its five over five for X cubed over three for
25
00:02:06.969 --> 00:02:12.560 A:middle L:90%
X for our plan. And then we have our
26
00:02:12.560 --> 00:02:17.539 A:middle L:90%
entwine zero and one. So score the next patient
27
00:02:17.539 --> 00:02:30.669 A:middle L:90%
plug those in, and then our ten of one
28
00:02:30.669 --> 00:02:36.500 A:middle L:90%
is pi over four. So that's from plugging in
29
00:02:36.500 --> 00:02:38.830 A:middle L:90%
the one. And then when we plug in zero
30
00:02:38.830 --> 00:02:43.340 A:middle L:90%
, all the terms are zero. So go ahead
31
00:02:43.340 --> 00:02:46.080 A:middle L:90%
and cancel those force and you get a minus pi
32
00:02:46.080 --> 00:02:50.009 A:middle L:90%
up here and had combined the remaining fractions. You
33
00:02:50.009 --> 00:02:53.300 A:middle L:90%
get twenty two over seven, and that's exactly what
34
00:02:53.300 --> 00:02:57.430 A:middle L:90%
we wanted to prove. So that's we've evaluated the
35
00:02:57.430 --> 00:02:58.889 A:middle L:90%
integral, and that's your final answer.