333 bai tich phan
TRANSCRIPT
333 BÀI TOÁN TÍCH PHÂN LUYỆN THI ĐẠI HỌC
1/ Cho hàm số : f(x)= x.sinx+x2 . Tìm nguyên hàm của hàm số g(x)= x.cosx
biết rằng nguyên hàm này triệt tiêu khi x=k
2/Định m để hàm số: F(x) = mx 3 +(3m+2)x2
-4x+3 là một nguyên hàm của hàm số:
f(x) = 3x2 +10x-4.
3/Tìm họ nguyên hàm của hàm số: f(x)= cos 3 x.sin8x.
TÍNH :
4/I = 3
2
4
3tg x dx
5/I = 4
2
6
(2cotg x 5)dx
6/I = 2
0
1 cos xdx
1 cos x
7/ I = 2
0
sin2 x.cos
2xdx
8/I = 3
0
(2cos2
x-3sin2 x)dx
9 / I = 2
2
sin( x)4 dx
sin( x)4
10 / I =
3
6
(tgx-cotgx)
2 dx
11/ I = 4
4
0
cos x dx
12 / I = 2
3
0
sin x dx
13*/ I =
3 32
3
sin x sin xcot gx dx
sin x
14/I = 2
4
0
sin x dx
15/I = 3
4
22
2cos
2sin
1
xx dx
16/I = 4
6
cotg2x dx
17/I = 22
sin x
4
e sin 2x dx
18/ I = 4
0
2
2
cos
x
e tgx
.
34/I =1
2 23
1dx
x 4 x
19/ I = 2
4
4sin
1
x dx
20/ I = 4
0
6cos
1
x dx
21/I = dxxxnsix )cos(2cos 442
0
22/ I = 2
3
0
cos xdx
23/ I =
32
0
4sin xdx
1 cosx
24/ I = 1
3 2
0
x 1 x dx
25/I =1
5 2
0
x 1 x dx
26/I =1
0
xdx
2x 1
27/I =1
x0
1dx
e 4
28/I =2
x1
1dx
1 e
29/I =
2x2
x0
edx
e 1
30/I =
x1
x0
edx
e 1
31/I =e
21
ln xdx
x(ln x 1)
32/I =
7
3
30
x 1dx
3x 1
33/I =2
3 2
0
(x 3) x 6x 8 dx
.
35/I =4
22
1dx
x 16 x
36*/I =6
22 3
1dx
x x 9
37/I =2
2 2
1
x 4 x dx
38/I =2
2 3
0
x (x 4) dx
39/I =
24
4 3
3
x 4dx
x
40*/I =
22
22
x 1dx
x x 1
41/I =ln 2
x
0
e 1dx
42/I =1
0
1dx
3 2x
43/I =2
5
0
sin xdx
44*/I =3
0
1dx
cos x
45/I =
2x1
x0
edx
e 1
46/I =ln 3
x0
1dx
e 1
47/I =4
2
6
1dx
sin x cot gx
48/I =
3 2e
1
ln x 2 ln xdx
x
.
49/I =e
1
sin(ln x)dx
x
50/I =1
3 4 5
0
x (x 1) dx
51/I =1
2 3
0
(1 2x)(1 3x 3x ) dx
52/I =2
31
1dx
x 1 x
53/I =3
2 2
6
tg x cot g x 2dx
54/I =1
2 3
0
(1 x ) dx
55*/I =1
2x0
1dx
e 3
56/I =
xln 3
x 30
edx
(e 1)
57/I =0
2x 3
1
x(e x 1)dx
58/I =2
6 3 5
0
1 cos x sin x.cos xdx
59*/I =2 3
25
1dx
x x 4
60/I =4
0
xdx
1 cos2x
61/I =
2xln 5
xln 2
edx
e 1
62/I =
2e
1
x 1.ln xdx
x
63/I =
21
0
xdx
(x 1) x 1
64/I =2
0
sin x.sin 2x.sin3xdx
65/I =2
4 4
0
cos2x(sin x cos x)dx
66*/I =2
3 3
0
( cos x sin x)dx
67/I =
73
8 42
xdx
1 x 2x
68*/I =2
0
4cos x 3sin x 1dx
4sin x 3cos x 5
69/I =9
3
1
x. 1 xdx
70/I =2
30
x 1dx
3x 2
71*/I =6
0
xsin dx
2
72*/I =2
0
xdx
2 x 2 x
73/I =3
3 2
0
x . 1 x dx
74**/I =1
20
ln(1 x)dx
x 1
75/I =2
0
sin xdx
sin x cos x
76/I =e
1
cos(ln x)dx
77*/I =2
2
0
4 x dx
78/I =2
1
xdx
1 x 1
.
79/I =e
1
1 3ln x ln xdx
x
80/I =3
2
2
ln(x x)dx
81/I =e
2
1
(ln x) dx
82/I =
2e
e
ln xdx
x
83/I =
2e
1
ln xdx
ln x
84/I =2
2
1
x ln(x 1)dx
85/I =3
23
1dx
x 3
86/I =1
20
1dx
4 x
87/I =
2
4
0
sin xdx
88/I =3
2
6
ln(sin x)dx
cos x
89/I =2
1
cos(ln x)dx
90*/I =2
2
0
ln( 1 x x)dx
91*/I =3
22
1dx
x 1
92/I =38
1
x 1dx
x
93/I =
33
21
xdx
x 16
.
94/I =6
20
cos xdx
6 5sin x sin x
95*/I =
2e
2e
1 1( )dx
ln xln x
96/I =3
2
4
x 4 dx
97/I =2
3 2
1
x 2x x 2 dx
98/I =
3
4
4
cos 2x 1dx
99/I =0
cos x sin xdx
100/I =2
0
1 sin xdx
101/I =
3
4
4
sin 2x dx
102/I =0
1 sin xdx
103/I =1 3
2
1
ln(x x 1) dx
104*/I =2
0
xsin xdx
1 cos x
105*/I =1
2 x1
1dx
(x 1)(4 1)
106*/I =
41
x1
xdx
1 2
107/I =
2
4
0
x sin xdx
108/I =
2
4
0
x cos xdx
109/I =6
2
0
x.sin x cos xdx
110*/I =
2 x1
20
x edx
(x 2)
111/I =2x 2
0
e sin xdx
112/I =2
2
1
1x ln(1 )dx
x
113/I =e
21
e
ln xdx
(x 1)
114/I =
1
2
0
1 xx.ln dx
1 x
115/I =
2t
1
ln xdx I 2
x
116/I =3
0
sin x.ln(cos x)dx
117/I =
2e2
1
cos (ln x)dx
118/I =4
0
1dx
cos x
119*/I =4
30
1dx
cos x
120/I =2
13 x
0
x e dx
121/I =22
sin x 3
0
e .sin x cos xdx
122/I =2
40
sin 2xdx
1 cos x
123/I =1
20
3dx
x 4x 5
124/I =2
21
5dx
x 6x 9
125/I =1
25
1dx
2x 8x 26
126/I =1
0
2x 9dx
x 3
127/I =4
21
1dx
x (x 1)
128*/I =0
2
2
sin 2xdx
(2 sin x)
129/I =1
20
x 3dx
(x 1)(x 3x 2)
130/I =1
30
4xdx
(x 1)
131/I =1
4 20
1dx
(x 4x 3)
132/I =
33
20
sin xdx
(sin x 3)
133/I =
33
6
4sin xdx
1 cos x
134/I =3
2
6
1dx
cos x.sin x
135/I =3
0
sin x.tgxdx
136/I = 3
4
1dx
sin 2x
.
137/I =
34
2 2 50
sin xdx
(tg x 1) .cos x
138/I =3
2 2
3
1dx
sin x 9cos x
139/I =2
2
cos x 1dx
cos x 2
140/I = 2
0
1 sin xdx
1 3cos x
141/I =2
0
cos xdx
sin x cos x 1
142/I = 4
21
1dx
x (x 1)
143/I =1
33
1dx
x 4 (x 4)
144/I =
33
0
sin xdx
cos x
145/I =1
0
x 1 xdx
146/I =6
4
x 4 1. dx
x 2 x 2
147/I = 0
21
1dx
x 2x 9
148/I =3
21
1dx
4x x
149/I = 2
2
1
4x x 5 dx
150/I = 2
22
2x 5dx
x 4x 13
151/I =1
x0
1dx
3 e
152/I =
1
4x 2x2
2x0
3e edx
1 e
153/I =4
27
1dx
x 9 x
154/I = 2
x 2
0
e sin xdx
155/I =
42
4 40
cos xdx
cos x sin x
156/I =1
0
3dx
x 9 x
157/I = 0
xsin xdx
158/I =2 2
0
x cos xdx
159/I =1
0
cos x dx
160/I =1
0
sin x dx
161/I =
2
4
0
x sin x dx
162/I =
2
4
0
x cos x dx
163/I =2
0
x cos xsin x dx
164/I = 6
2
0
x cos xsin x dx
165/I =4
x
1
e dx
166/I =4
3x
0
e sin 4x dx
167/I =2x 2
0
e sin x dx
168/I =
2 x1
20
x edx
(x 2)
169/I =e
1
(1 x) ln x dx
170/I =e
2
1
x ln x dx
171/I =
1
e2
1
ln x dx
172/I =e
1
x(2 ln x)dx
173/I =
2e
2e
1 1( )dx
ln xln x
174/I =2
2
1
(x x)ln x dx
175/I =2
2
1
1x ln(1 )dx
x
176/I =2
51
ln xdx
x
177/I =e
21
e
ln xdx
(x 1)
178/I =
1
2
0
1 xx ln dx
1 x
179/I =2
3
cos x.ln(1 cos x)dx
180/22
sin x 3
0
e sin x cos x dx
181/I= 2
40
sin 2xdx
1 sin x
.
182/I =2
40
sin 2xdx
1 cos x
183/I =2
21
5dx
x 6x 9
184/I =
21
0
x 3x 2dx
x 3
185/I =4
21
1dx
x (x 1)
186/I =1
20
ln(1 x)dx
x 1
187/I
41
60
1 xdx
1 x
188/I =1
15 8
0
x 1 x dx
189/I =
x1
x x0
edx
e e
190/I= e
1
e
ln x dx
191/I =2
sin x
0
(e cos x)cos x dx
192/I =2
0
sin 2x.cos xdx
1 cos x
193/I =2
0
sin 2x sin xdx
1 3cos x
194/I =
24
0
1 2sin xdx
1 sin 2x
195/I =
5 33
20
x 2xdx
x 1
196/I =3
2
4
tgxdx
cos x 1 cos x
197/I =2
2
1
x 1( ) dxx 2
198/I =4
2
0
x.tg x dx
199/I =5
3
( x 2 x 2 )dx
200/I =4
1
2dx
x 5 4
201/I =2
1
xdx
x 2 2 x
202/I =2
21
ln(1 x)dx
x
203/I =2
0
sin 2xdx
1 cos x
204/I =
20082
2008 20080
sin xdx
sin x cos x
205/I =2
0
sin x.ln(1 cos x)dx
206/I =
23
21
x 1dx
x
207/I =
34
20
sin xdx
cos x
208/I =2
2
0
cos x.cos4x dx
209/I =1
2x x0
1dx
e e
210/I =e
21
e
ln xdx
(x 1)
211/I =1
0
1dx
x 1 x
212/I =
21
20
xdx
4 x
213/I =1
20
xdx
4 x
214/I =
1
42
20
xdx
x 1
215/I =2
0
sin 3xdx
cos x 1
216/I =
2
22
20
xdx
1 x
217/I =
22
41
1 xdx
1 x
218/I =
37
3 20
xdx
1 x
219/I =
xln 2
x0
1 edx
1 e
220/I =1
0
x 1 x dx
221/I =1
2
0
x 1dx
222/I =2
3 3
0
(cos x sin x)dx
223/I =
23
0
x 1dx
x 1
224/I =1
2 2x
0
(1 x) .e dx
225/I =2
20
cos xdx
cos x 1
226/I =
7
3
30
x 1dx
3x 1
.
227/I =2
6
1 sin 2x cos2xdx
cos x sin x
228/I =
x 21
2x0
(1 e )dx
1 e
229/I =3
2 3
0
x (1 x) dx
230/I =
32
20
sin x.cos xdx
cos x 1
231/I =
1
2
20
4x 1dx
x 3x 2
232*/I =2
0
xsin x.cos xdx
233/I =2
0
cos xdx
cos 2x 7
234/I =4
21
1dx
x (x 1)
235/I =2
2 3
0
sin 2x(1 sin x) dx
236/I =2
30
x 1dx
3x 2
237/I =4
27
1dx
x x 9
238/I =3 4
0
xsin x cos xdx
239/I =2
3
2
cos x cos x cos xdx
240*/I =1
2
1
ln( x a x)dx
241/I =2
x0
1 sin xdx
(1 cos x)e
242/I =2
0
sin 2x sin xdx
cos3x 1
243/I =4
2 20
sin 2xdx
sin x 2cos x
244/I =
2
32
20
xdx
1 x
245/I =
2
32
20
xdx
1 x
246/I =
21
22
2
1 xdx
x
247/I =
21
20
xdx
4 x
248/I =2
22
3
1dx
x x 1
249/I =1
5 3 6
0
x (1 x ) dx
250/I =2
0
sin xdx
1 sin x
251/I =2
0
cos xdx
7 cos 2x
252/I =4
21
1dx
(1 x)x
253/I =2
30
x 1dx
3x 2
254*/I =3
4
cos x sin xdx
3 sin 2x
.
255/I =2
3
2
cos x cos x cos xdx
256/I =3
4
4
tg xdx
257*/I =2
x
0
1 sin xe dx
1 cos x
258/I =1
2 3
0
(1 x ) dx
259/I =4
2
0
x.tg xdx
260/I=2
2 20
1dx
(4 x )
261/I =
21
30
3xdx
x 2
262*/I =
52
51
1 xdx
x(1 x )
263/I =3
20
cos xdx
1 sin x
264/I =
23
60
sin xdx
cos x
265/I =
36
0
sin x sin xdx
cos2x
265/I =2
3
1dx
sin x 1 cos x
266/I =3
6 21
1dx
x (1 x )
.
267/I =2
20
sin xdx
cos x 3
268/I =
2
0
sin xdx
x
269/I =2
2
0
sin x cos x(1 cos x) dx
270/I =
4 44
0
sin x cos xdx
sin x cos x 1
271/I =
4 44
0
sin x cos xdx
sin x cos x 1
272/I =2
0
sin x cos x cos xdx
sin x 2
273/I =
1
1 x
3a
edx
x
274/I =
3 21
20
x 2x 10x 1dx
x 2x 9
275/I =
31
2 30
xdx
(x 1)
276/I =1
30
3dx
x 1
277*/I =
41
60
x 1dx
x 1
278/I =1
30
xdx
(2x 1)
279/I =7
2
1dx
2 x 1
280/I =
3
2
21
2
1dx
x 1 x
.
281*/I =
21
20
x ln(x 1 x )dx
1 x
282/I =4
2
1
(x 1) ln x dx
283/I =3
2
0
x ln(x 1)dx
284/I =
32
21
3xdx
x 2x 1
285/I =1
3 20
4x 1dx
x 2x x 2
286/I =
1
2
21
2
1dx
(3 2x) 5 12x 4x
287/I =1
0
1dx
x 1 x
288/I =2
0
cos xdx
2 cos 2x
289/I =2
4
cos x sin xdx
3 sin 2x
290/I =2
3 3
0
(cos x sin x)dx
291/I =2
5 4
0
cos xsin xdx
292/I =2
4 4
0
cos2x(sin x cos x)dx
293/I =2
0
1dx
2 sin x
294/I =2
0
1dx
2 cos x
295/I =2
22
3
1dx
x x 1
296/I =
37
3 20
xdx
1 x
297*/I =2
31
1dx
x 1 x
298/I =
31
20
xdx
x 1 x
299/I =1
21
1dx
1 x 1 x
300/I =3
4
6
1dx
sin x cos x
301/I =2
0
cos xdx
cos x 1
302/I =2
0
cos xdx
2 cos x
303/I =2
0
sin xdx
sin x 2
304/I =
32
0
cos xdx
cos x 1
305/I = 2
0
1dx
2cos x sin x 3
306/I = 2
2
3
cos xdx
(1 cos x)
307/I =4
3
0
tg x dx
.
308*/I =1
2x1
1dx
3 e
309*/I =
2
x
sin xdx
3 1
310*/I =2
0
sin xdx
cos x sin x
311/I =
42
4 40
sin xdx
cos x sin x
312*/I =2
20
tgxdx
1 ln (cos x)
313*/I =2
0
sin xdx
cos x sin x
314*/I =1
x 21
1dx
(e 1)(x 1)
315*/I =1
3x 1
0
e dx
316*/I =
21
20
xdx
x 4
317*/I =
32
4 20
cos xdx
cos 3cos x 3
318*/Tìm x> 0 sao cho
2 tx
20
t edt 1
(t 2)
319*/I =3
2
4
tan xdx
cos x cos x 1
320*/I =1
2
0
3x 6x 1dx
321*/I =4
5
0
tg x dx
322/I =4
3
6
cotg x dx
323/I = 3
4
4
tg x dx
324*/I = 4
0
1dx
2 tgx
325/I =
52
0
sin xdx
cos x 1
326/I =3
2
6
cos 2xdx
1 cos 2x
327*/I =4
2
0
t gx 1( ) dx
tgx 1
328*/I =1
31
2
xdx
x 1
329*/I =
3 32
41
x xdx
x
330/I =
xln 3
x x0
edx
(e 1) e 1
331/I =
14e
21
e
1dx
x cos (ln x 1)
333*/I =4
0
ln(1 tgx)dx
