Variant №1 Ratsional funksiyalarni integrallash
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6a-19 uchun yakuniy nazorat variantlari 020620101313
Variant №1 1. Ratsional funksiyalarni integrallash. 2. O’zgarmas koeffitsientli chiziqli bir jinsli bo’lmagan differensial tenglama. 3. Integralni toping: ∫ + − 1 7 2 2
x dx 4. Aniq integralni hisoblang: 5. Differensial tenglamani yeching: Variant №2 1. Aniq integralning geometriyaga tatbiqi. 2. Bir jinsli funksiyalar va bir jinsli differensial tenglamalar. 3. Integralni toping: ∫ − + 6 2 2 x x dx 4. Aniq integralni hisoblang: 5. Differensial tenglamani yeching: Variant №3 1. Dekart va qutb koordinatalar sistemasida soha yuzasini hisoblash. 2. Mavjudlik va yagonalik teoremasi. 3. Integralni toping: ∫ + + 7 2 5 2
x dx 4. Aniq integralni hisoblang: 5. Differensial tenglamani yeching: 2 2 3 x y y = ′ Variant №4 1. Dekart koordinatalar sistemasida egri chiziq yoyi uzunligini hisoblash. 2. Differensial tenglamalar. Asosiy ta’rif va tushunchalar. 3. Integralni toping: ∫ + − 1 2 2 2
x dx 4. Aniq integralni hisoblang: 5. Differensial tenglamani yeching: 0 2 = + + ′ y y y Variant №5 1. To’g’ridan-to’g’ri integrallash usuli. 2. O’zgaruvchilari ajraladigan differensial tenglamalar. 3. Integralni toping: ∫ + − 2 11 2 2
x dx 4. Aniq integralni hisoblang: 5. Differensial tenglamani yeching: x xy y + = ′ 2 Variant №6 1. Aylanish jismining hajmini hisoblash. 2. O’zgarmas koeffitsientli chiziqli bir jinsli bo’lmagan differensial tenglama. 3. Integralni toping: ∫ + + 2 2 2 x x dx 4. Aniq integralni hisoblang: 5. Differensial tenglamani yeching: ( ) 2 1 2 y x e y x + = ′ ∫ 2 0 cos
π xdx x y x e y 4 2 − = ′ ∫ 2 0 sin π
x 1 ) 0 ( , sin cos
= = + y dx xdx y xdy ( ) ∫ − 1 0 4 1 dx e e x x ∫ + 1 0 2 1 4
x arctgx ∫ − 2 0 cos ) 5 ( π xdx х ∫ 2 1 ln xdx x Variant №7 1. O’zgaruvchini almashtirish va bo’laklab integrallash yordamida aniq integralni hisoblash. 2. Umumiy va xususiy yechim. 3. Integralni toping: ∫ + − 3 12 3 2
x dx 4. Aniq integralni hisoblang: 5. Differensial tenglamani yeching:
Variant №8 1. Trigonometrik funksiyalarni integrallash. 2. Bernulli tenglamasi. 3. Integralni toping: ∫ + x x dx 3 2 2 4. Aniq integralni hisoblang: 5. Differensial tenglamani yeching: ( ) 0 1 1 = ′ + + y e y
Variant №9 1. Irratsional funksiyalarni integrallash. 2. Tartibini pasaytirish mumkin bo’lgan yuqori tartibli tenglamalarning ba’zi bir tiplari. 3. Integralni toping: ∫ + − 5 5 2 x x dx 4. Aniq integralni hisoblang: 5. Differensial tenglamani yeching: Variant №10 1. Nyuton-Leybnits formulasi. 2. Birinchi tartibli differensial tenglamalar. 3. Integralni toping: ∫ − − 2 4 3 2
x dx 4. Aniq integralni hisoblang: 5. Differensial tenglamani yeching:
Variant №11 1. Ratsional kasrlarni eng sodda kasrlarga yoyish yo’li bilan ratsional funksiyani integrallash. 2. Bir jinsli funksiyalar va bir jinsli differensial tenglamalar. 3. Integralni toping: 4. Aniq integralni hisoblang: 5. Differensial tenglamani yeching:
Variant №12 1. Cheksiz va uzluksiz funksiyalarning xosmas integrallari. 2. O’zgarmas koeffitsientli chiziqli bir jinsli differensial tenglama. 3. Integralni toping: 4. Aniq integralni hisoblang: 5. Differensial tenglamani yeching: ∫ π 2 0 3 cos xdx x 1 2 2 − = ′ y y yx ∫ 1 0 3
xe x ∫ 2 0 2 cos sin π
x 1 ) 0 ( , − = = ′ y x e y ∫ 4 0 3 cos sin π
x x 1 2 2 − = ′ y y yx dx x ∫ 2 cos 2 ∫ + 2 1 4 2
dx ( ) 0 2 2 = − + dy x dx y ( ) ∫ −
x x 3 2 2 1 ∫ 4 0 5 cos sin
π dx x x ( ) 0 2 2 2 = + − ydy dx x Variant №13 1. Irratsional funksiyalarni integrallash. 2. Boshlang`ich va chegaraviy shartlar. 3. Integralni toping: 4. Aniq integralni hisoblang: 5. Differensial tenglamani yeching: Variant №14 1. Nyuton-Leybnits formulasi. 2. O’zgarmas koeffitsientli chiziqli bir jinsli differensial tenglama. 3. Integralni toping: ∫ + + 1 5 3 2
x dx 4. Aniq integralni hisoblang: 5. Differensial tenglamani yeching: Variant №15 1. Ratsional funksiyalarni integrallash. 2. O’zgarmas koeffitsientli chiziqli bir jinsli bo’lmagan differensial tenglama. 3. Integralni toping: ∫ + − 1 7 2 2
x dx 4. Aniq integralni hisoblang: 5. Differensial tenglamani yeching: Variant №16 1. Aniq integralning geometriyaga tatbiqi. 2. Bir jinsli funksiyalar va bir jinsli differensial tenglamalar. 3. Integralni toping: ∫ − + 6 2 2 x x dx 4. Aniq integralni hisoblang: 5. Differensial tenglamani yeching: Variant №17 1. Dekart koordinatalar sistemasida egri chiziq yoyi uzunligini hisoblash. 2. Differensial tenglamalar. Asosiy ta’rif va tushunchalar. 3. Integralni toping: ∫ + − 1 2 2 2
x dx 4. Aniq integralni hisoblang: 5. Differensial tenglamani yeching: 0 2 = + + ′ y y y Variant №18 1. To’g’ridan-to’g’ri integrallash usuli. 2. O’zgaruvchilari ajraladigan differensial tenglamalar. 3. Integralni toping: ∫ + − 2 11 2 2
x dx 4. Aniq integralni hisoblang: 5. Differensial tenglamani yeching: x xy y + = ′ 2 ∫ − dx x x 4 3 1 1
x ∫ 4 1 y x y y 2 1 − = ′ x t dx x = − ∫ 2 9 4 , 1 1 1 2 2 − = ′ y y yx ∫ 2 0 cos
π xdx x y x e y 4 2 − = ′ ∫ 2 0 sin π
x 1 ) 0 ( , sin cos
= = + y dx xdx y xdy ∫ + 1 0 2 1 4
x arctgx ∫ − 2 0 cos ) 5 ( π xdx х Variant №19 1. O’zgaruvchini almashtirish va bo’laklab integrallash yordamida aniq integralni hisoblash. 2. Umumiy va xususiy yechim. 3. Integralni toping: ∫ + − 3 12 3 2
x dx 4. Aniq integralni hisoblang: 5. Differensial tenglamani yeching:
Variant №20 1. Trigonometrik funksiyalarni integrallash. 2. Bernulli tenglamasi. 3. Integralni toping: ∫ + x x dx 3 2 2 4. Aniq integralni hisoblang: 5. Differensial tenglamani yeching: ( ) 0 1 1 = ′ + + y e y
Variant №21 1. Irratsional funksiyalarni integrallash. 2. Tartibini pasaytirish mumkin bo’lgan yuqori tartibli tenglamalarning ba’zi bir tiplari. 3. Integralni toping: ∫ + − 5 5 2 x x dx 4. Aniq integralni hisoblang: 5. Differensial tenglamani yeching:
№22 1. Ratsional kasrlarni eng sodda kasrlarga yoyish yo’li bilan ratsional funksiyani integrallash. 2. Bir jinsli funksiyalar va bir jinsli differensial tenglamalar. 3. Integralni toping: 4. Aniq integralni hisoblang: 5. Differensial tenglamani yeching:
Variant №23 1. Cheksiz va uzluksiz funksiyalarning xosmas integrallari. 2. O’zgarmas koeffitsientli chiziqli bir jinsli differensial tenglama. 3. Integralni toping: 4. Aniq integralni hisoblang: 5. Differensial tenglamani yeching: Variant №24 1. Boshlang’ich funksiya va aniqmas integralning ta’rifi, xossalari. 2. Chiziqli differensial tenglama. 3. Integralni toping: ∫ + + 17 2 2 x x dx 4. Aniq integralni hisoblang: 5. Differensial tenglamani yeching: ( ) x x ye y e = ′ + 1
∫ π
0 3 cos xdx x 1 2 2 − = ′ y y yx ∫ 1 0 3
xe x ∫ 2 0 2 cos sin π
x 1 ) 0 ( , − = = ′ y x e y dx x ∫ 2 cos 2 ∫ + 2 1 4 2
dx ( ) 0 2 2 = − + dy x dx y ( ) ∫ −
x x 3 2 2 1 ∫ 4 0 5 cos sin
π dx x x ( ) 0 2 2 2 = + − ydy dx x dx x ∫ + 3 4 4 3 2 1 1 Variant №25 1. Integrallash usullari. 2. O’zgaruvchilari ajraladigan differensial tenglamalar. 3. Integralni toping: ∫ + + 4 101 2 x x dx 4. Aniq integralni hisoblang: 5. Differensial tenglamani yeching: 1 2 + = ′ y y x Variant №26 1. Cheksiz va uzluksiz funksiyalarning xosmas integrallari. 2. Umumiy va xususiy yechim. 3. Integralni toping: 4. Aniq integralni hisoblang: 5. Differensial tenglamani yeching: tgx y y ) 1 2 ( + = ′
Variant №27 1. Irratsional funksiyalarni integrallash. 2. Boshlang`ich va chegaraviy shartlar. 3. Integralni toping: 4. Aniq integralni hisoblang: 5. Differensial tenglamani yeching: Variant №28 1. O’zgaruvchini almashtirish va bo’laklab integrallash yordamida aniq integralni hisoblash. 2. Birinchi tartibli differensial tenglamalar. 3. Integralni toping: 4. Aniq integralni hisoblang: 5. Differensial tenglamani yeching: Variant №29 1. O`rniga qo`yib (o’zgaruvchilarni almashtirib) integrallash usuli. 2. Tartibini pasaytirish mumkin bo’lgan yuqori tartibli tenglamalarning ba’zi bir tiplari. 3. Integralni toping: ∫ + − 4 5 4 2
x dx 4. Aniq integralni hisoblang: 5. Differensial tenglamani yeching: Variant №30 1. Nyuton-Leybnits formulasi. 2. O’zgarmas koeffitsientli chiziqli bir jinsli differensial tenglama. 3. Integralni toping: ∫ + + 1 5 3 2
x dx 4. Aniq integralni hisoblang: 5. Differensial tenglamani yeching: xdx e ∫ 1 ln ( ) ∫ +
x x 3
x ∫ 3 1 3 ∫ − dx x x 4 3 1 1
x ∫ 4 1 y x y y 2 1 − = ′ ∫ −
x x 4 3 dx x ∫ 4 0 4 sin π ( ) 0 2 2 2 = + − ydy dx x dx e x ∫ 3 0 3
y x = ′ x t dx x = − ∫ 2 9 4 , 1 1 1 2 2 −
′ y y yx Document Outline
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