โจทย์การหาปริพันธ์และพื้นที่.pdf
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E-learning 25 -02-55
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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
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E-learning 25 -02-55
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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
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E-learning 25 -02-55
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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. . .
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E-learning 25 -02-55
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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
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E-learning 25 -02-55
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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