Giáo án Giải tích 12 chương III (Ban cơ bản)

 


I. 
 !"#$ %&'#$ 
#$%()*+ +(++!,+(++-.% +(++!
/+012
3!-'4#$% #$% %5678'4$+(++
!-9:#$%2
-;!<=6 #-;>?@4%(A6B#$CD -; %'4
E4FE:+GEA "-(H>H!#$4IE4-)% /-J:K%$
4$I DJL-JJ+%$4<M;2
(6:(6>4 >G+>G*N D>4'E4FE:%?2
  
a. !"#$%&!'&E: HO D"-+ D"-K
( )$%'!*$(+
- C4D4 % (AP +" QRI% DO 677IG+ Q
 ,-./0
a. 1$2+$!34&5+S
( /674
8 9:8;<= 9:>8;<? 
T2UCVWXURYZ[Y\UR]R^2
_2U

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b,<1-(HI>#$
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I<;f

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c,<1E:DAgh%]

%C,<1eb,<1i]j>;
#$c,<1Ef
`Ub,<1>;#$
c,<1E:I
#$c,<1E-KJ6'b,<1i] 
DA]>h%f

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∫
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b,<1#$c,<1 D:6b,<1ebd,<16<
ec,<16<2

2!"#$
i!"_
k
, 1 , 1f x dx f x C= +
∫
i!"
, 1 , 1 , 1kf x dx k f x dx k= ≠
∫ ∫
i!"l
m , 1 , 1n , 1 , 1f x g x dx f x dx g x dx± = ±
∫ ∫ ∫

l2&'#$
$/$G-a>ol%$
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Ef


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R4'-;r
RM4%$
R4'-;_RM:%
b,<1%$44bd,<1ec,<12q
$sc,<1el<
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 
CDADAR%;
6-a?$%$
CDA4R%D6
_,C E$l1-9R%9
Eu-a?$D/$2
R4'-;
vM:L
#$
%-ME4D!67_2

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6-a>o_%$
R4'-;l
vM6$D4!"
bd,<1ec,<1O4'-;D/$
>OE-9
-a>oD/$2
CDADAR%;
6-a>o%$
CDADAR%+0
C E$p -9
R%9Eu;6-a>o
D/$2
CDA4R%D6
,C E$p1-9R%9Eu
-a>oD/$2
CDADAR%+0
C E$r -9
R%9Eu;6!"
D/$2
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9Eu!"D/$2
R4'-;p
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"D/$2
CDA4R%D6r
,C E$w1-9R%9Eu
!"D/$2
?::%b,<1#$

%
$sc,<1el<
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%jDB4!
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1. Trong các cặp hàm số dới đây, hàm số
nào là nguyên hàm của hàm số còn
lại ?
a)
x
e
và


x
e
;
b) sin2x và sin
2
x ;
c)
2
2
1
x
e
x


ữ

và

4
1 .
x
e
x


ữ

2. Tìm nguyên hàm của các hàm số
sau :
a) f(x) =
3
1x x
x
+ +
;
b) f(x) =
2 1
x
x
e

;
c) f(x) =
2 2
1
sin .cosx x
;
d) f(x) =

sin 5 . cos3x x
;
e) f(x) = tan
2
x ;
g) f(x) =
3
2
1
1
x
x
+

;
h) f(x) =
3 2 x
e
;
i) f(x) =
+
1
(1 )(1 2 )x x
.
3. Sử dụng phơng pháp đổi biến số, hãy
tính :
a)
9
(1 ) dx x

(đặt
= 1 )u x
;
b)
3
2
2
(1 ) dx x x+

(đặt
2
1 )u x= +
;
c)
3
cos sin dx x x

(đặt
cos )t x=
;
d)

+ +

d
2
x x
x
e e
(đặt

x
u e=
).
4. Sử dụng phơng pháp tính nguyên
$s!,@
<
1deF$-J$
>G-(H-K:
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8D:%$4
]4R4'
-;=>'
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n
m
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=
t
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n
m
a
a

a

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( )
L
x
e


e
x
e


x
e

>
;#$
x
e

D
( )

L
x
e



e
x
e


x
e

>
;#$
x
e

1
x
C
M$
>;
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1
x
e
x

N
5
>;
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x
e
x
C
C
5







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x
xx

++=
++

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C
O
5
e
r y
l w l
l w l
r y
x x x C
+ + +
1


dx
e

x
x
5C
e









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e
x
x
C
e
> _
,> _1
x
x
C
e
+
+

61
ECM$QBM$

C
5
ORMSM$ xxxx
+=
( )

+=
xdxxdxxdxx CM$QM$
C
5
ORMSM$
Cxx
+






+=
CRMQRM
N
5
N
5
1
l
_

x

e C

+
1
_ _ _
, 1
,_ 1,_ 1 l _ _ x x x x
= +
+ +
[G$J
_ _
, 1 >
l _
x
F x C
x
+
= +

qlR%%?>
$1
_
,_ 1
t
_
x
C

+
1

r


_
,_ 1
r
x C
+ +
1
p
_
4%
p
c x C +
61
_
_
x
C
e
+
+
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NU
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