2-Kurs talabalari uchun "Oliy matematika" fanidan test topshiriqlari

49. 
    ³_^{x2  1} _ ni sodda kasrlar yig’indisiga yoying.
    

10. 
    x²  4
    

2



x 1

1



11x

A)

;

B) *

;

x

x^2  4

4x

4x2  4

C)

2



x 1

;

D)

1



11

.

x

x^2  4

4x

xx2  4

50.

Jadval intеgrallardan noto’g’risini ko’rsating.

A)

 x ^k dx 

x k 1

 C ;

В) ctgxdx  ln | sin x | C;

k 1

С)

* 

dx

 arcsin x  C;

D) 

dx

 tgx  C .

1

2

2

 x

cos

x

51.

f (x) 1 

1

funksiyaning boshlang’ich funksiyalardan birini toping.

cos^2 3x

A)

x 

1

ctgx 1;

B) x 

1

ctgx  2 ;

C)

x 

1

tgx 1;

D) * x 

1

tg3x  4 .

3

3

3

3

52.

f (x)  1 

1

funksiyaning boshlang’ich funksiyasini toping.

sin ^2 4x

A)

x 

1

tg4x  C ;

B) x 

1

tg 4x  C ;

C) x 

1

ctg 4x  C ;

D)* x 

1

ctg 4x  C .

4

4

4

4

53. Quyidagi funksiyalardan qaysi biri uchun F(x)  2cos x  sin x  C funksiya

boshlang’ich funksiya bo’ladi?

A) f (x) 2sin x  cos x ;

B) f (x)  2sin x  cos x ;

C) f (x)  2sin x  cos x ;

D) * f (x) 2sin x  cos x .

54. F(x)  xe^ ^x

 sin x  C funksiya quyidagi funksiyalardan qayi biri uchun

bohlang’ich funksiya bo’ladi?

A)

f (x)  (1  x)e^ ^x  cos x ;

B) f (x)  (1  x)e^ ^x  cos x ;

C)

f (x)  e^ ^x  cos x ;

D) * f (x)  (1  x)e^ ^x  cos x .