9-bob. Aniq integral

2. Aniq integralni hisoblash usullari

1. 
   Agar y=f(x) funksiya [a,b] kesmada uzluksiz bo‘lsa, unda yuqori chegarasi o‘zgaruvchi bo‘lgan aniq integral orqali aniqlanadigan
   

funksiya xossasi qayerda to‘g‘ri ko‘rsatilgan ?
A) . B) . C) .
D) . E) .

2. 
   aniq integralni Nyuton–Leybnits formulasi bilan hisoblashda quyidagi amallardan qaysi biri bajarilmaydi ?
   

A) f(x) funksiyaning biror F(x) boshlang‛ich funksiyasi topiladi.
B) boshlang‘ich funksiyaning F(a) va F(b) qiymatlari hisoblanadi.
C) F(b)+F(a) yig‘indi hisoblanadi.
D) F(b)– F(a) ayirma hisoblanadi.
E) ko‘rsatilgan barcha amallar bajariladi .

3. 
   Agar y=F(x) berilgan [a,b] kesmada y=f(x) funksiyaning boshlang‛ich funksiyasi bo‘lsa, unda aniq integral uchun Nyuton–Leybnits formulasi qayerda to‘g‘ri ifodalangan ?
   

A) . B) . C) .
D) . E) .

4. 
   aniq integralning qiymatini Nyuton–Leybnits formulasi yordamida toping.
   

A) 1. B) 0. C) 1/2. D) –1. E) 2/3.

5. 
   aniq integralning qiymatini Nyuton–Leybnits formulasidan foydalanib aniqlang.
   

A) 0. B) 1. C) 2/3. D) 0.75. E) –0.3.

6. 
   aniq integralning qiymatini Nyuton–Leybnits formulasi yordamida hisoblang.
   

A) π . B) π/2 . C) π/3 . D) π/4 . E) π/6 .

7. 
   aniq integral qiymatini Nyuton–Leybnits formulasi yordamida toping.
   

A) π . B) π/2 . C) π/3 . D) π/4 . E) π/6 .

8. 
   aniq integralni bo‘laklab integrallash formulasi yordamida
   

hisoblash jarayonida quyidagi amallardan qaysi biri bajarilmaydi ?
A) u=u(x) funksiyaning du differensiali hisoblanadi.
B) dv=dv(x) differensial bo‘yicha v=v(x) funksiya topiladi.
C) u(b)v(b)+ u(a)v(a) yig‘indi hisoblanadi.
D) integral hisoblanadi.
E) ko‘rsatilgan barcha amallar bajariladi.

9. 
   Aniq integralni bo‘laklab integrallash formulasi qayerda to’g’ri yozilgan?
   

A) . B) . C) .
D) . E) .

10. 
    aniq integral qiymatini bo‘laklab integrallash formulasi yordamida toping.
    

A) π . B) π/2 . C) π/3 . D) π/4 . E) π/6 .

11. 
    aniq integralni bo‘laklab integrallash formulasi yordamida hisoblang.
    

A) e . B) e/2 . C) 1 . D) 0.5 . E) 2 .

12. 
    aniq integralni o‘zgaruvchilarni almashtirish formulasi orqali hisoblashda quyidagi amallardan qaysi biri bajarilmaydi ?
    

A) x=φ(t) almashtirma tanlanadi.
B) φ(t)=a va φ(t)=b tenglamalarning yechimlari α va β topiladi.
C) f[φ(t)] murakkab funksiya tuziladi.
D) almashtirmaning hosilasi φ′(t) hisoblanadi.
E) ko‘rsatilgan barcha amallar bajariladi.

13. 
    aniq integralni x=(t) almashtirma orqali hisoblash formulasini ko‘rsating.
    

A) . B) .
C) . D) .
E) .

14. 
    aniq integralni hisoblash uchun qaysi almashtirmadan foydalanish mumkin?
    

A) x=t² . B) x²=t . C) x=sint . D) sinx=t . E) sinx²=t .

15. 
    aniq integral qiymatini o‘zgaruvchilarni almashtirish usulida hisoblang.
    

A) . B) π/2 . C) 0 . D) 1 . E) π .

16. 
    aniq integral qiymatini hisoblash uchun qaysi almashtirmadan foydalanish mumkin?
    

A) t=1/x. B) . C) . D) . E) .