Ma’ruzalar: № “ Calculus” fanidan ma’ruza mavzulari soat
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2019 2020 сиртки Шахсий топшириқ f23b228d362d0af70757ef85d99058dc
- Bu sahifa navigatsiya:
- Yechilishi.
- 13-tоpshiriq.
- 10- tоpshiriq.
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11-tоpshiriq. Qutb
kооrdinаtаsidа bеrilgаn chiziqlаr bilаn
chеgаrаlаngаn figurа yuzini hisоblаng: 3 cos 4 r .
Yechilishi. 2 1 2 , ) ( 2 1 d r S
. 0 3 cos , 0 3 cos
4 , , 3 2 6 3 2 6 , 2 2 3 2 2
n n n Z n n n
21
. 4 ) 0 6 1 6 0 0 ( 24 ) 6 sin
6 1 ( 24 ) 6 cos 1 ( 24 3 cos 16 2 1 6 0 6 / 0 6 / 0 6 2 d d S
■ 12-tоpshiriq. Pаrаmеtrik tеnglаmа оrqаli bеrilgаn chiziqning yoy uzunligini hisоblаng.
. 2 0 ), cos (sin 4 ), sin (cos
4 t t t t y t t t x
Yechilishi.
. sin
4 ) sin cos (cos
4 , cos 4 ) cos sin sin
( 4
t t t t t y t t t t t t x
. 8 2 2 2 4 sin 16 cos 16 , ) ( ) ( 2 2 0 2 2 0 2 0 2 2 2 2 2 2 t tdt dt t t t t l dt y x l t t ■
o‘qi аtrоfidа аylаnishidаn hоsil bo‘lgаn jism hаjmini tоping.
. 2 , 2 2
y x x y
Bеrilgаn funksiyаlаr kеsishish nuqtаlаrini tоpаmiz: . 2 ; 1 0 2 3 ; 2 2 2 1 2 2 x x x x x x x
22
. 5 4 2 1 1 5 1 8 8 8 16 5 32 4 2 5 1 ) 4 4 3 4 ( ) 4 4 4 4 ( ) 2 ( ) 2 ( . 2 1 2 3 4 5 2 1 2 3 4 2 1 2 1 2 2 3 4 2 2 2 2 x x x x x dx x x x x dx x x x x x dx x x x V dx y V b a
10- tоpshiriq. Аniqmаs intеgrаllаrni hisоblаng.
10.1 а) 2 . 1 dx x x b)
3 4 3 .
x e dx
d) 3 2 3 6 13 6 . ( 2)( 2) x x x dx x x
10.2 а) 1 ln
. x dx x b) arctg 4 1 .
x dx d) 3 2
6 13 8 . ( 2) x x x dx x x
10.3 а) 2 . 1 dx x x
b) 3 3 4 . x x e dx
d) 3 2 3 6 13 6 . ( 2)( 2) x x x dx x x
10.4 а) 3 2 2 . 1 x dx x b)
4 sin 2
. x xdx d) 3 2
6 13 7 . ( 1)( 2) x x x dx x x
10.5 а) 2 2 ln . x x dx x b)
2 cos 2 .
xdx d) 3 2
6 14 10 . ( 1)( 2) x x x dx x x
10.6 а) 2 1 cos
. ( sin ) x dx x x
b) arctg 6 1 .
x dx d) 3 2
6 14 6 . ( 1)( 2) x x x dx x x
10.7 а) 4 2 . 1 xdx x x
23
b) 2 4 3 . x e x dx
d) 3 2 3 6 11 10 . ( 2)( 2) x x x dx x x
10.8 а) 2 cos sin
. sin
x x x dx x x b)
sin 4 .
xdx d) 3 2
6 10 10 . ( 1)( 2) x x x dx x x
10.9 а) 3 2 arccos
1 . 1 x dx x
b) 3 5 2 . x x e dx d) 3 2
6 11 7 . ( 1)( 2) x x x dx x x
10.10 а) 3 4 . 1 x x dx x
b) 2 1 6 .
x e dx d)
3 2 . 2 x x dx x x
10.11 а) tg ln cos .
b) 2 . cos xdx x
d) 3 2 3 2 6 7 2 . ( 1)
x x dx x x 10.12 а) 4 2
1 xdx x x
b) 3 2 9 . x e x dx
d) 3 2 3 6 13 8 . ( 2) x x x dx x x 10.13 а)
2 tg 1 . cos 1 x dx x
b) 2 ln 4 . x dx d)
3 2 1 . 1
x dx x x
10.14 а) 3 . 1 xdx x b)
arctg 3 1 .
x dx d) 3 2
3 9 10 2 . ( 1)( 1)
x x dx x x
10.15 а) 2 1 2
1 .
dx x x
b) arctg 5 1 .
x dx d) 3 2
2 6 7 4 . ( 2)( 1)
x x dx x x
10.17 а) 2 3 4 2 . ( 6 5) x dx x x
b)
5 7 sin 2 .
xdx
d) 3 2 3 2 6 4 10 . ( 4)( 1)
x x dx x x
10.18 а) 4 2 2 . 2
x x
b)
3 5 3 . x e x dx
d) 2 3 4 55 34 . ( 2)(
2) x x dx x x 10.19 а) 2 4arctg
. 1
x dx x
b) 3 2 cos5 .
xdx d)
3 2 3 2 6 7 1 . ( 1)( 1)
x x dx x x
10.20 а) 2 2 arccos
. 1
x dx x
24
b) 2 3 5 . x x e dx d) 3 2
14 29 19 . ( 1)( 2) x x x dx x x
10.21 а) 2 . 2 1 dx x x b)
5 7 4 . x x e dx
d) 3 2 3 2 10 23 26 . ( 2)( 2)
x x dx x x
10.22 а) tg ln cos .
xdx
b) 2 . cos xdx x
d) 3 2 3 2 6 7 2 . ( 1)
x x dx x x 10.23 а) 3 2
. x dx x b) arctg 3 4
x dx d) 3 2
6 13 8 . ( 2) x x x dx x x 10.24 а)
2 arctg
. 1
x dx x
b)
2 3 cos 2 .
xdx d) 3 2
2 6 5 . ( 2)( 1) x x x dx x x 10.25 а) 2 cos
. 2sin
x x dx x x
b)
5 4 3 . x x e dx
d) 3 2 3 6 13 6 . ( 2)( 2) x x x dx x x
10.26 а) 2 sin . 2cos
x x dx x x
b) 4 7 cos3 .
xdx d)
2 3 3 3 9 . ( 2)(
1) x x dx x x 10.27 а) 3 2cos
3sin . (2sin 3cos ) x x dx x x
b) 2 5 cos 4 .
xdx d)
3 2 3 2 6 5 4 . ( 2)( 1)
x x dx x x
10.28 а) 2 2sin
3cos . (2cos 3sin ) x x dx x x
b) 3 4 cos 2 .
xdx d) 3 2
2 6 4 4 . ( 3)( 1)
x x dx x x
10.30 а) 2 5arc tg
3 . 1 c x x dx x
b) 2 3 ln .
xdx d)
3 2 3 3 3 . ( 2)(
1) x x x dx x x |
