Tải bản đầy đủ (.doc) (15 trang)

Gián án Bài tập Tích phân

Bạn đang xem bản rút gọn của tài liệu. Xem và tải ngay bản đầy đủ của tài liệu tại đây (94.52 KB, 15 trang )

TuyÓn tËp c¸c bµi to¸n tÝch ph©n
1.
2
1
x x
0
(2x 1)e dx



(§H Dîc_81 )
2. Víi
x 0;
4
π
 

 
 
x¸c ®Þnh a,b sao cho
1 a cos x bcos x
cos x 1 sin x 1 sin x
= +
− +

3. TÝnh
/ 4
3
0
dx dx
I J


cos x
cos x

π
= =

(§H BK TH_82)
4.
/ 2
0
sin x cos x 1
dx
sin x 2cosx 3
π
− +
+ +

(Bé §Ò)
5.
1
3
0
(3x 1)dx
(x 3)
+
+

(Bé §Ò)
6.
1

3
0
xdx
(x 1)+

(Bé §Ò)
7.
1
2
4
0
x 1
dx
x 1

+

(Bé §Ò)
8.
2x 2
0
e sin xdx
π

(Bé §Ò)
9.
/ 2
0
cos xdx
2 cos2x

π
+

(Bé §Ò)
10.
1
2
1
dx
x 2x cos 1
,(0< < )

α π
− α +

(Bé §Ò)
11.
2a
2 2
a
x a dx ,(a>0)−

(Bé §Ò)
12.
/ 2
3
0
4sin xdx
1 cos x
π

+

(Bé §Ò)
13.
a
2 2
0
x a dx+

(Bé §Ò)
14.
2
0
1 sin xdx
π
+

(Bé §Ò)
15.
3 /8
2 2
/8
dx
sin x cos x
π
π

(Bé §Ò)
16.
2

1
dx
x 1 x 1+ + −

(Bé §Ò)
17. Gpt
x
2
0
(u x )du sin x− =

(Bé §Ò)
18.
b
2
1
x ln xdx

(BK_94)
19.
/ 2
2
0
x cos xdx
π

(BK_94)
20.
2
2

2 / 3
dx
x x 1−

(BK_95)
21.
0
cos x sin xdx
π

(BK_98)
22. Cho hµm sè:
f(x) sin x.sin2x.cos5x=
a. T×m hä nguyªn hµm cña g(x).
b. TÝnh tÝch ph©n:
2
x
2
f(x)
I dx
e 1
π
−π
=
+

(BK_99)
23.
ln 2
2x

x
0
e
dx
e 1+

(BK_00)
24.
1
2
0
x 1
dx
x 1

+

(XD_96)
25.
/ 4
0
cos x 2sin x
dx
4cos x 3sin x
π
+
+

(XD_98)
26.

1
3
0
3dx
1 x+

(XD_00)
27.
1
4 2
0
dx
x 4x 3+ +

(§H Má_95)
28.
/ 3
2 2
/ 6
tg x cot g x 2dx
π
π
+ −

(§H Má_00)
29.
/ 3
/ 6
dx
sin xsin(x / 6)

π
π
+ π

(§H Má_00)
30.
6 6
/ 4
x
/ 4
sin x cos x
dx
6 1
π
−π
+
+

(§H Má_01)
31.
2
2
1
ln(x 1)
dx
x
+

(§H Hµng H¶i_00)
32.

/ 2
3
sin xdx
sin x cos x
π
+

(§H GT VT_95)
33.
3
5 2
0
x . 1 x dx+

(§H GT VT_96A)
34.
1/ 9
3x
2 5
0
x 1
5 dx
4x 1
sin (2x 1)
 
+ +
 ÷

+
 


(§H GT VT_97)
35.
7 / 3
3
0
x 1
dx
3x 1
+
+


x
2
4
2
(10 sin x)dx

− π

(§H GT VT_98)
36.
1 3
1 0
x
I dx x.arctgxdx
5 4x

= +


∫ ∫
(§H GT VT_99)
37.
/ 2
2
/ 2
x cos x
dx
4 sin x
π
−π
+


(§H GT VT_00)
38.
/ 2
3
0
5cosx 4sin x
dx
(cosx sin x)
π

+

(§H GT VT_01)
39.
/ 2

4
4 4
0
cos x
dx
cos x sin x
π
+

(§H GTVT HCM_99)
40.
/ 3
2
6
/ 4
sin x
dx
cos x
π
π

(§H GTVT HCM_00)
41.
2
2
2
2
x 1
dx
x x 1



+
+

(HV BCVT_97)
42.
/ 2
3
2
0
sin x cos x
dx
1 cos x
π
+

(HV BCVT_98)
43.
1
4
x
1
x
dx
1 2

+

(HV BCVT_99)

44.
2
0
xsin x cos xdx
π

(HV NH_98)
45.
/ 2
2 2
0
I cos x cos 2xdx
π
=


/ 2
2 2
0
J sin x cos 2xdx
π
=

(HV NH HCM_98)
46.
/ 3
2
0
x sin x
dx

cos x
π
+


1
3
2
0
x
dx
x x 1+ +

(HV NH HCM_00)

1 4
2
2
0 0
sin 4x
x ln(x 1)dx dx
1 cos x
+
+
∫ ∫
47.
2
0
1 sin xdx
π

+

(§H NTh¬ng_94)
48.
1 1
2
2 2
0 0
dx x 3x 2
dx
x 3
(x 3x 2)

+ +
+
+ +
∫ ∫
(§H NTh¬ng_99)
49.
( )
/ 4
3
0
cos2x
dx
sin x cosx 2
π
+ +

(§H NTh¬ng_00A)

50.
1
3 2
2
0
x 2x 10x 1
dx
x 2x 9
+ + +
+ +

(§H NTh¬ng_00)
1
2
2
0
x 3x 10
dx
x 2x 9
+ +
+ +

51.
/ 4
6 6
0
sin 4x
dx
sin x cos x
π

+

(§H NTh¬ng_01A)
52.
2
5
2
2
I ln(x 1 x ) dx

 
= + +
 
 

(§H KT_95)
53.
1
5 3 6
0
x (1 x ) dx−

(§H KT_97)
54.
/ 4
4 2
0
dx
I dx
cos x x 1

1
5
0
x
J=
π
=
+
∫ ∫
(§H TM_95)
55.
1
0
x 1 xdx−

(§H TM_96)
56.
7 ln 2
9 x
x
3
2
0 0
x 1 e
I dx dx
1 e
1 x
J=

=

+
+
∫ ∫
(§H TM_97)
57.
ln2
x
0
dx
e 5+

(§H TM_98A)
58.
4
2
1
dx
x (1 x)+

(§H TM_99)
59.
/ 2
3
0
4sin x
dx
(sin x cos x)
π
+


(§H TM_00)
60.
11
0
sin xdx
π

(HV QHQT_96)
61.
/ 4
2 4
0
sin x cos xdx
π

(§H NN_96)
62.
e
2
1/ 2
ln x
dx
(1 x)+

(§H NN_97)
63.
/ 4
2
0
cos x cos4xdx

π

(§H NN_98)
64.
7 / 3
3
0
x 1
dx
3x 1
+
+

(§H NN_99)
65.
1
2 2
0
(1 x x ) dx− −

(§H NN_01D)
66.
/ 2
x 2
0
e cos xdx
π

(§H Thuû Lîi_96)
67.

0
1 cos2xdx
π
+

(§H Thuû Lîi_97)
68.
3 2
2
4 2 5
1 1
x 1 dx
I dx
x x 1 x(x 1)
J=
+
=
+ + +
∫ ∫
(§H Thuû Lîi_99)
69.
( )
/ 4
0
ln 1 tgx dx
π
+

(§H Thuû Lîi_01A)
70.

/ 2
2 2
0
3sin x 4cos x
dx
3sin x 4cos x
π
+
+

(§H Thuû Lîi_00)
3
3 2
0
x 2x xdx− +

71.
/ 4
0
sin x.cosx
dx
sin2x cos2x
π
+

(§H V¨n Hãa_01D)
72.
/ 2
2 2 2 2
0

sin x cos x
dx a,b 0
a cos x b sin x
;
π

+

(HV TCKT_95)
73.
2 / 2
2
2
0
x
dx
1 x−

(HV TCKT_97)
74.
/ 4
2
0
x(2cos x 1)dx
π


(HV TCKT_98)
75.
/ 3

2
/ 4
cos x sin x 1
dx dx
3 sin 2x
x 1
1
4
0
x

π
π
+ +
+
+
∫ ∫
(HV TCKT_99)
/ 2
4 3
0 0
sin x 7cos x 6
dx x cos x sin xdx
4sin x 3cos x 5

π π
+ +
+ +
∫ ∫
76.

1
4 2
0
x
dx
x x 1+ +

(HV TCKT_00)
77.
/ 2
2
0
(x 1)sin xdx
π
+

(§H Më_97)
78.
/ 2
3
0
4sin x
dx
1 cos x
π
+

(§H Y HN_95)
79.
1 1

2
2x x
1/ 2 0
dx
1 x dx
e e



+
∫ ∫
(§H Y HN_98)
80.
4 / 3
dx
x
sin
2
π
π

(§H Y HN_99)
81.
/ 3 2
2
4
2
/ 4 1
x
tg xdx dx

x 7x 12

π
π
− +
∫ ∫
(§H Y HN_00)
82.
3
2
2
x 1dx−

(§H Y HN_01B)
83.
1
2
0
x 1dx+

(§H Y TB_97B)
84.
/ 4
2
0
dx
2 cos x
π



(§H Y TB_00)

×