E-learning 25 -02-55

1

1. 2( ) ( ) (1 )F x f x x ( )F x (Ent. 2 2/2542)

1. 3

2

3

xx x c 2. 2(1 )x c

3. 22 2x x c 4. 3(1 )

3

xc

2. f ( ) 2 1f x x f 1

2 1x

f (Ent. 1 1/2546) 1. 1 2. 1

3 3. 0 4. 1

3

3. R 1sin

(4 3) 0x dx

cos 2 (Ent. 1 1/2542)

1. 0 32

2. 0 32

3. 1 12

4. 1 1

4. ( )y f x 3 2x 3 7 0x y (1, 4) 2( ) ( )g x x f x 21 g (x) dx (Ent. 2/2547 1) 1. 5 2. 7 3. 8 4. 10

E-learning 25 -02-55

2

5. f (0) 1 (1)f f (0) 1f 1

1( ) 6f x dx

( 1)f (Ent. 1/2547 1 )

1. 7 2. 1 3. 13 4. 15

6. 3 1

2 25 3

( ) 12 2

f x x x ( )y f x

1. 5 3

2 2( ) 2f x x x x 2. 5 3

2 25 3

( ) 22 2

f x x x x

3. 5 3

2 25 3

( ) 22 2

f x x x 4. 5 3

2 2( ) 2f x x x

7. 2

(4 1)( 1)( )

x xF x dx

x

( ) 0F x

1. 1x x 2. 1 4

x x

3. 1 14

x x

4. 1 0x x 104

x

E-learning 25 -02-55

3

8. 3 2( ) ( 5)dg x x xdx

( ) d xh xdx

( ) ( ) g x h x dx

1. 5 3

2 23 2

5 3x x c 2.

5 32 2x x c

3. 3 1

2 23 3

4 4x x c 4.

3 1

2 23

4x x c

9. 4

( )4

xf x x a 2 1( )

4

a

af x dx

( )f a

1. 12

2. 12

3. 32

4. 32

10. f g 1,3 ( ) ( ) 1f x g x x ( ) 0g x 1,3x . 3

1( ) 2f x dx .

3 2

1

8( ( ) ( ))

3f x g x dx

1. . . 2. . . 3. . . 4. . .

E-learning 25 -02-55

4

11. f f 0,1 4( )( ) 1f x

g xx

(1) (1) 1f f (0) (0) 2f f 10

( ) g x dx

1. 52

2. 12

3. 32

4. 72

12. 7 23y x x 1. 7 5 0x y 2. 7 5 0x y 3. 7 3 0x y 4. 7 3 0x y

13. 2( ) ( )g x x f x ( ) 2 3f x x (1) 0g (4)f 1. 0 2. 11 3. 13 4. 28

14. ( )f x ( )g x 1( ( ))( )

f g xg x

( (0)) 5f g ( (2))f g 1. 1 2. 3 3. 5 4. 7

E-learning 25 -02-55

5

15. f 4,0

16. a b f 4 3 2( ) 2f x x x x ax b ( )Q x 2( ) ( ( ))f x Q x

1

0( ) f x dx

1. 7130

2. 3130

3. 1130

4. 130

17. ( )y f x 2 3 0x y (0,3) 20

( ) 3f x dx ( ) 2g x x ( )f x (2) 0g (2)f

3

3 , 1( )

2 , 1

x xf x

x x