Microsoft Word Олий матем 2-cem. Ma'Ruza маътинлари docx



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9.44
5
4
9.45
3
13
ln
9.46
9
2
9.48
0
9.48
4
9.49
7
1
arctg
9.50
3
3

9.51
2
3
3


9.52
16
2
a

9.53
1
2
ln
2

9.54
a
12

9.55


2
1
ln

9.56
6

9.58


12
4
7
32
3
3

9.58
4

9.59
1
cos
1

9.60
 
 
2
ln
3
ln
th
th

9.61
6

9.62
27
3
80
9.63
2

9.64


1
ln

e
9.65
27
3
8
6


9.66
2
ln
7
2
11

9.68
5
,
1
ln
9.68
2
3
2
9.69
. 9
9.80
. 100/28
9.81.
2+2ln3
9.82
. 8+2ln2
9.83

4 9.84.
2
9.85
.6
9.86
.2
9.88
.
а
)
0
1
1
0
cos
2
cos
cos
0
sin
sin
sin
;
cos
;
cos
2
0
2
0
2
0
2
0























x
xdx
x
x
x
xdx
d
dx
du
x
u
xdx
x
 
в
)
ln4-1
9.88



4
/
1
2

e
9.89
.e-2
9.80

2
ln
3
/


9.81



e
e
/
5
2

9.82



1
5
,
0


e
9.83
.4
9.84

2
/


9.85
. 0,25
9.86
.0
9.88.
2/3
9.88

2
/
2


9.89.
2
3
arctg
arctg

9.90

5
/

9.91





9
/
7
2
7
ln/

9.92

2
/
3
1
6
/



9.93.
5
,
1
ln
5
,
0
9.94



1
4
ln
5
,
1

9.95

2
ln
5
,
0
5
,
0

9.96

8
/
81

9.97


2
ln
1
2

9.98
3
/
32
9.99


5
1
2
1
2
ln


9.100
2
1
3
2
ln
5
2
2




9.101
2
1
1
ln
2



e
e
9.102
2
3
3
8

9.103
72
3
9.104
4
1


9.105
4

9.106
3
3

9.108
3
/
32
9.108
ab

9.109


ph
2
2
a asosning h balandligi ko’paytmasining 2/3 qismi.
9.110
3
/
32
9.111
2
ln
8
9.112
1
9.113
3
16
9.114
2
,
19
9.115
6
,
25
9.116
15
8
8
9.118
3
8
9.118
3
5
20
9.119
2
a

9.120
8
,
0
9.121




t
a
x
a
2
2
sin
2
2
4



9.122


a
e
e
a
h
s
a
35
,
2
2
1
2
1
2






9.123
2
3
a

9.124
8
/
3
2
a

9.125
2
a
9.126
2
/
3
2
a

9.128
3
/
32
9.128

1
2

e
9.129

15
/
2
16
9.130
. 4,5 
9.131
. 4ln2-2/3
9.132
.8/12
9.133
.8/6
9.134.
0,5
9.135
. 44/15
9.136

1/3+ln3
9.138
. 3/ln2-4/3
9.138.
0,5
9.139
. 15/3
9.140
. 1/3
9.141
.3
9.142
. 18/12
9.143
а

Bernulli 
lemniskatasi bilan chegaralangan sohani yuzini toping (9.8-chizma).
Yechish:












4
/
0
4
/
0
2
2
2
2
0
1
2
cos
2
2
cos
2
1
4
4






a
a
d
a
d
a
S
S
 
 
9.8 – chizma
.



4

S



в
)
a

2
9.144
а
)
(8.8 - chizma) kardioidaning yoyi uzunligini toping.
 
 
 
 
9.9 – chizma. 




a
a
d
a
d
a
d
a
a
d
a
a
l
l
8
2
sin
2
4
2
cos
2
2
2
cos
2
2
2
cos
2
2
2
cos
1
sin
2
2
0
0
0
2
0
2
2
0
2
2
2



































в
)
a
6
9.145
27
/
670
9.146
a
8
9.148
o’qlar 
bilan 
kesishish 
nuqtalari 
0
1

t
va 
3
1
4
1
;
8
3
8
0
4
4
2
4





dt
t
t
S
t
9.148


3
2
ln
6


9.149
1
2
h
9.150 
2
2
5
/
13
4
/
3
2
1
,
1
t
x
dx
x
x
S





deb olamiz :
2
ln
35
.
1
1
1
ln
2
1
1
15
6
.
2
25
.
1
5
/
13
4
/
3
2
2














t
t
t
dt
t
t
S
9.151
.O’qlar bilan 
kesish nuqtalari
0
1

x
va 
3
2


x




3
2
ln
sin
1
sin
cos
cos
cos
3
/
0
2
3
/
0
2
3
/
0












x
x
d
x
xdx
x
dx
S
9.152


2
1
ln
2


9.153
5
,
1
ln
5
,
0
1

9.154


1
ln
2


e
e
9.155
8
9.156 
27
/
7

9.158 

3
9.158 

18
9.159 
5
/
6

9.160
2
4
R

9.161
3
/
14

9.162


2
2
2

sh
a

9.163







3
3
4
1
2


9.164




2
1
ln
2
2



9.165
2
3
64
a

9.166

3
9.168
ab
2
4

9.168
15
/
256
;
24
/
1024


9.169
2
2
;
2
/


9.180


24
;
12
9.181
3
/
64
;
15
/
128


9.182


40
;
5
/
112
9.183


8
;
15
/
544
9.184




2
/
1
;
2
2


e
e


9.185
15
/
256
;
3
/
2
32


9.186


5
3
112
3
128
;
3
/
52

9.188


15
148
;
30
397
9.188 
a
)


3
ln
5
,
0
3
ln
1
ln
2
1
3
1
ln
1
1
lim
ln
2
1
3
1
ln
1
1
ln
lim
2
1
1
1
ln
2
1
lim
1
lim
1
1
2
2
2
2
2









































b
b
b
b
x
x
x
dx
x
dx
b
b
b
b
b
b) 1
9.189
a












 












2
/
2
/
ln
lim
4
2
ln
lim
cos
lim
cos
0
2
/
0
2
/
0
0
2
/
0
0











tg
x
tg
x
dx
x
dx
.
b
)uzoqlashuvchi
9.180
a
)
;
3
4
3
4
3
4
3
2
2
2
1
2
3
1
2











x
x
dx
x
x
dx
x
x
dx
integral ostidagi funksiya 
1

x
va 
3

x
larda aniqlanmagan. Bu 
integrallarni alohida-alohida hisoblaymiz.








;
2
/
1
arcsin
0
lim
2
arcsin
lim
2
1
lim
3
4
0
2
1
0
2
1
2
0
2
1
2




























x
x
dx
x
x
dx








.
2
/
0
1
arcsin
lim
2
arcsin
lim
2
1
lim
3
4
0
3
2
0
3
2
2
0
3
2
2




























x
x
dx
x
x
dx
Demak, 









2
2
3
4
3
1
2
x
x
dx
. b)uzoqlashuvchi

e

x
0


9.181











chi
uzoqlashuv
anda
bo
n
n
x
dx
anda
bo
n
n
lg
'
1
1
1
lg
'
1
1

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