Aniq integral tatbiqlari
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ANIQ INTEGRAL TATBIQLARI
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- Mustaqil yechish uchun misollar
ANIQ INTEGRAL TATBIQLARI
Misol. x 2 +y 2 =8 aylana y=x 2 /2 bilan ikki qismga bo’lingan. Ikkala qismini yuzasini toping.
Yechish: Grafiklar kesishish nuqtalarini topamiz: 2 2 8 2 1
x 2 4 8 4
x 2 4 8 4
x 0 4 32 4 2 x x
, 2 1 x
, 2 2 x
2 2 8 2 r r S d 3 4 2 2 2 6 8 2 1 8 arcsin 4 ) 8 ( 3 2 2 2 2 1 П x x x x dx x S (kv.birl.) 3 4 6 3 4 2 8 1 2
S S d (kv.birl.)
Misol. y=2-x 2 va y 3 =x 2 egri chiziqlar bilan chegaralangan figuraning yuzini toping:
Yechish: Egri chiziqlar kesishish nuqtalarini topamiz: 3 2 2 2 x x 2 6 4 2 6 12 8
x x x
0 8 13 6 2 4 6
x x
, 1 1 x
, 1 2 x
,,y
3 =x 2
2
1 1 1 1 3 5 3 3 2 2 15 32 5 3 3 1 2 5 3 3 1 2 5 3 3 2 2
x x dx x x S (kv.birl.) Misol. y=x
parabolalar bilan chegaralangan figurani Ox o‘qi atrofida aylantirishdan hosil bo‘lgan jism hajmini hisoblang: Yechish:
2 2 y x x y sistemasidan kesishish nuqtalarini topamiz: 1 ,
, 1 , 0 2 1 2 1 y y x x
) . ( 10 3 5 1 2 1 0 1 5 2 1 0 5 2 4 1 0 2 1 birlik kub x x dx x xdx V V V
Misol. 3 2 ) 1 ( 3 2 x y yarim kubik parabolaning 3 2 x y
bilan chegaralangan yoy uzunligini hisoblang: Yechish: Egri chiziqlarning kesishish nuqtasini aniqlaymiz: 3 )
( 3 2 3 x x , 1 2 3 ), 1 ( ) 1 ( 3 2 , 3 2 , 2 `
y holda u x x y chunki y да x
2 1 2 1 ) 2 2 5 5 ( 9 2 2 1 3 2 1 2 ) 1 ( 2 3 1 2 dx x dx x L
Mustaqil yechish uchun misollar: Berilgan chiziqlar bilan chegaralangan figuralar yuzalarini hisoblang: 1. 2
x y va Ox o’q bilan 2.
2 ) 1 ( x y va
1 2 2 2 y x
3. chiziqlar bilan chegaralangan figuraning yuzini toping.
Egri chiziqlar yoylari uzunliklari hisoblansin: 4. 0 , cos ln 1 x x y dan
6 x gacha 5.
0 , cos 8 sin
6 , cos 6 sin
8 t t t y t t x dan
2 t gacha 6.
0 , 2 , 3 1 2 3 t t y t t x dan 3 t gacha 7.
2 , 4 2 2 y y x chiziqlar bilan chegaralangan figurani Oy o‘qi atroqida aylantirishdan hosil bo‘lgan jismning hajmini toping. 8. 0
1 , 1 1 2 y x x y chiziqlar bilan chegaralangan figurani Ox o‘qi atrofida aylantirishdan hosil bo‘lgan jismning hajmini toping. 9. 1
y parabolani y=0, x=-1, x=4 to‘g‘ri chiziqlar bilan chegaralangan figuraning yuzini toping. 10.
2 ) 1 ( x y va
1 2 2 2 y x chiziqlar bilan chegaralangan figuraning yuzini toping.
11. ) ln(sin x y egri chiziqning 3 x dan
2 x gacha bo‘lgan yoyning uzunligini toping. 12.
, 1 , 4 , 1 , 4 y x x xy chiziqlar bilan chegaralangan figurani Ox o‘qi atrofida aylantirishdan hosil bo‘lgan jismning hajmini hisoblang. Download 224.69 Kb. Do'stlaringiz bilan baham: |
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