- Trang chủ >>
- Đề thi >>
- Đề thi lớp 7
Dang Toan Tich Phan Cuc Hay
Bạn đang xem bản rút gọn của tài liệu. Xem và tải ngay bản đầy đủ của tài liệu tại đây (132.1 KB, 13 trang )
<span class='text_page_counter'>(1)</span><div class='page_container' data-page=1>
<b>333</b>
<b> </b>
<b> BÀI TOÁN TÍCH PHÂN LUYỆN THI ĐẠI HỌC</b>
<sub></sub>
1/ Cho hàm số : f(x)= x.sinx+x2<sub> . Tìm nguyên hàm của hàm số g(x)= x.cosx </sub>
biết rằng nguyên hàm này triệt tiêu khi x=k <i>π</i>
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<sub> +10x-4.</sub>
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 x
dx
1 cos x
7/ I =
<sub></sub>
0
<i>π</i>
2
❑ sin2 x.cos2xdx
8/I =
<sub></sub>
0
<i>π</i>
3
❑ (2cos2 x-3sin2 x)dx
9 / I =
2
2
sin( x)
4 <sub>dx</sub>
sin( x)
4
10 / I =
<i>−π</i>
6
<i>π</i>
3
❑ (tgx-cotgx)2 dx
11/ I =
4
4
0
cos x dx
19/ I =
<sub></sub>
<i>π</i>
4
<i>π</i>
2
1
sin4<i><sub>x</sub></i> dx
12 / I =
2
3
0
sin x dx
13*/ I =
3 3
2
3
sin x sin x
cot gx dx
sin x
14/I =
2
4
0
sin x dx
15/I =
<i>π</i>
4
<i>π</i>
3
1
sin2<i>x</i>
2cos
2<i>x</i>
2
dx
16/I =
<sub></sub>
<i>π</i>
6
<i>π</i>
4
❑ cotg2x dx
17/I =
2
2
sin x
4
e sin 2x dx
18/ I =
<sub></sub>
0
<i>π</i>
4
<i>e</i>tgx+2
cos2<i><sub>x</sub></i>
<b>.</b>
34/I =
1
2 2
3
1
dx
x 4 x
35/I =
4
2
2
1
dx
x 16 x
</div>
<span class='text_page_counter'>(2)</span><div class='page_container' data-page=2>
20/ I =
<sub></sub>
0
<i>π</i>
4
1
cos6<i><sub>x</sub></i> dx
21/I =
si
cos 2<i>x</i>(¿<i>n</i>4<i>x</i>+cos4<i>x</i>)dx
0
<i>π</i>
2
¿
22/ I =
2
3
0
cos xdx
23/ I =
3
2
0
4sin x
dx
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
x
dx
2x 1
27/I =
1
x
0
1
dx
e 4
28/I =
2
x
1
1
dx
1 e
29/I =
2x
2
x
0
e
dx
e 1
30/I =
x
1
x
0
e
dx
e 1
31/I =
e
2
1
ln x
dx
x(ln x 1)
32/I =
7
3
3
0
x 1
dx
3x 1
33/I =
2
3 2
0
(x 3) x 6x 8 dx
<b>.</b>
36*/I =
6
2
2 3
1
dx
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 =
2
4
4 3
3
x 4
dx
x
40*/I =
2
2
2
2
x 1
dx
x x 1
41/I =
ln 2
x
0
e 1dx
42/I =
1
0
1
dx
3 2x
43/I =
2
5
0
sin xdx
44*/I =
3
0
1
dx
cos x
45/I =
2x
1
x
0
e
dx
e 1
<sub></sub>
46/I =
ln 3
x
0
1
dx
e 1
47/I =
4
2
6
1
dx
sin x cot gx
48/I =
3 2
e
1
ln x 2 ln x
dx
x
<b>.</b>
64/I =
2
0
sin x.sin 2x.sin 3xdx
</div>
<span class='text_page_counter'>(3)</span><div class='page_container' data-page=3>
49/I =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
3
1
1
dx
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
2x
0
1
dx
e 3
56/I =
x
ln 3
x 3
0
e
dx
(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
2
5
1
dx
x x 4
60/I =
4
0
x
dx
1 cos 2x
61/I =
2x
ln 5
x
ln 2
e
dx
e 1
62/I =
2
e
1
x 1
.ln xdx
x
63/I =
2
1
0
x
dx
(x 1) x 1
65/I =
2
4 4
0
cos 2x(sin x cos x)dx
66*/I =
2
3 3
0
( cos x sin x )dx
67/I =
7
3
8 4
2
x
dx
1 x 2x
68*/I =
2
0
4cos x 3sin x 1
dx
4sin x 3cos x 5
69/I =
9
3
1
x. 1 xdx
70/I =
2
3
0
x 1
dx
3x 2
71*/I =
6
0
x
sin dx
2
72*/I =
2
0
x
dx
2 x 2 x
73/I =
3
3 2
0
x . 1 x dx
74**/I =
1
2
0
ln(1 x)
dx
x 1
75/I =
2
0
sin x
dx
sin x cos x
76/I =
e
1
cos(ln x)dx
77*/I =
2
2
0
4 x dx
78/I =
2
1
x
dx
1 x 1
</div>
<span class='text_page_counter'>(4)</span><div class='page_container' data-page=4>
79/I =
e
1
1 3ln x ln x
dx
x
80/I =
3
2
2
ln(x x)dx
81/I =
e
2
1
(ln x) dx
82/I =
2
e
e
ln x
dx
x
83/I =
2
e
1
ln x
dx
ln x
84/I =
2
2
1
x ln(x 1)dx
85/I =
3
2
3
1
dx
x 3
86/I =
1
2
0
1
dx
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
2
2
1
dx
x 1
92/I =
3
8
1
x 1
dx
x
94/I =
6
2
0
cos x
dx
6 5sin x sin x
95*/I =
2
e
2
e
1 1
( )dx
ln x
ln 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
<sub></sub> <sub></sub>
104*/I =0 2
x sin x
dx
1 cos x
105*/I =
1
2 x
1
1
dx
(x 1)(4 1)
106*/I =
4
1
x
1
x
dx
1 2
107/I =
2
4
0
x sin xdx
</div>
<span class='text_page_counter'>(5)</span><div class='page_container' data-page=5>
93/I =1 2
x
dx
x 16
<b>.</b>
109/I =
6
2
0
x.sin x cos xdx
110*/I =
2 x
1
2
0
x e
dx
(x 2)
111/I =
2x 2
0
e sin xdx
112/I =
2
2
1
1
x ln(1 )dx
x
113/I =
e
2
1
e
ln x <sub>dx</sub>
(x 1)
114/I =
1
2
0
1 x
x.ln dx
1 x
115/I =
2
t
1
ln x
dx I 2
x
116/I =
3
0
sin x.ln(cos x)dx
117/I =
2
e
2
1
cos (ln x)dx
upload.123doc.net/I =
4
0
1
dx
cos x
119*/I =
4
3
0
1
dx
cos x
120/I =
2
1
3 x
0
x e dx
108/I =
4
0
x cos xdx
123/I =
1
2
0
3
dx
x 4x 5
124/I =
2
2
1
5
dx
x 6x 9
125/I =
1
2
5
1
dx
2x 8x 26
126/I =
1
0
2x 9
dx
x 3
127/I =
4
2
1
1
dx
x (x 1)
128*/I =
0
2
2
sin 2x
dx
(2 sin x)
129/I =
1
2
0
x 3
dx
(x 1)(x 3x 2)
130/I =
1
3
0
4x
dx
(x 1)
131/I =
1
4 2
0
1
dx
(x 4x 3)
132/I =
3
3
2
0
sin x
dx
(sin x 3)
133/I =
3
3
6
4sin x
dx
1 cos x
134/I =
3
2
6
1
dx
cos x.sin x
</div>
<span class='text_page_counter'>(6)</span><div class='page_container' data-page=6>
121/I =
2
2
sin x 3
0
e .sin x cos xdx
122/I =
2
4
0
sin 2x
dx
1 cos x
137/I =
3
4
2 2 5
0
sin x
dx
(tg x 1) .cos x
138/I =
3
2 2
3
1
dx
sin x 9cos x
139/I =
2
2
cos x 1
dx
cos x 2
140/I =
2
0
1 sin x
dx
1 3cos x
141/I =
2
0
cos x
dx
sin x cos x 1
142/I =
4
2
1
1
dx
x (x 1)
143/I =
1
3
3
1
dx
x 4 (x 4)
144/I =
3
3
0
sin x
dx
cos x
145/I =
1
0
x 1 xdx
146/I =
6
4
x 4 1
. dx
x 2 x 2
147/I =
0
2
1
1
dx
x 2x 9
135/I =
3
0
sin x.tgxdx
136/I =
3
4
1
dx
sin 2x
<b>.</b>
152/I =
1
4x 2x
2
2x
0
3e e
dx
1 e
153/I =
4
2
7
1
dx
x 9 x
154/I =
2
x 2
0
e sin xdx
155/I =
4
2
4 4
0
cos x
dx
cos x sin x
156/I =
1
0
3
dx
x 9 x
157/I = 0
x sin 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
</div>
<span class='text_page_counter'>(7)</span><div class='page_container' data-page=7>
148/I =1 2
1
dx
4x x
149/I =
2
2
1
4x x 5 dx
150/I =
2
2
2
2x 5
dx
x 4x 13
151/I =
1
x
0
1
dx
3 e
167/I =
2x 2
0
e sin x dx
168/I =
2 x
1
2
0
x e
dx
(x 2)
169/I =
e
1
(1 x)ln x dx
170/I =
e
2
1
x ln x dx
171/I =
1
e
2
1
ln x dx
172/I =
e
1
x(2 ln x)dx
173/I =
2
e
2
e
1 1
( )dx
ln x
ln x
174/I =
2
2
1
(x x)ln x dx
175/I =
2
2
1
1
x ln(1 )dx
x
176/I =
2
5
1
ln x<sub>dx</sub>
x
177/I =
e
2
1
e
ln x
dx
(x 1)
163/I =
2
0
x cos x sin x dx
164/I =
6
2
0
x cos x sin x dx
165/I =
4
x
1
e dx
166/I =
4
3x
0
e sin 4x dx
182/I =
2
4
0
sin 2x
dx
1 cos x
183/I =
2
2
1
5
dx
x 6x 9
184/I =
2
1
0
x 3x 2
dx
x 3
185/I =
4
2
1
1
dx
x (x 1)
186/I =
1
2
0
ln(1 x)
dx
x 1
187/I
4
1
6
0
1 x
dx
1 x
188/I =
1
15 8
0
x 1 x dx
189/I =
x
1
x x
0
e
dx
e e
190/I=
e
1
e
ln x dx
191/I =
2
sin x
0
(e cos x)cos x dx
</div>
<span class='text_page_counter'>(8)</span><div class='page_container' data-page=8>
178/I =
1
2
0
1 x
x ln dx
1 x
179/I =
2
3
cos x.ln(1 cos x)dx
180/
2
2
sin x 3
0
e sin x cos x dx
181/I=
2
4
0
sin 2x
dx
1 sin x
<b>.</b>
197/I =
2
2
1
x 1
( ) dx
x 2
198/I =
4
2
0
x.tg x dx
199/I =
5
3
( x 2 x 2 )dx
200/I =
4
1
2
dx
x 5 4
201/I =
2
1
x
dx
x 2 2 x
202/I =
2
2
1
ln(1 x)
dx
x
203/I =
2
0
sin 2x
dx
1 cos x
204/I =
2008
2
2008 2008
0
sin x
dx
sin x cos x
205/I =
2
0
sin x.ln(1 cos x)dx
192/I =
2
0
sin 2x.cos x
dx
1 cos x
193/I =
2
0
sin 2x sin x
dx
1 3cos x
194/I =
2
4
0
1 2sin x
dx
1 sin 2x
195/I =
5 3
3
2
0
x 2x
dx
x 1
196/I =
3
2
4
tgx
dx
cos x 1 cos x
212/I =
2
1
2
0
x
dx
4 x
213/I =
1
2
0
x
dx
4 x
214/I =
1
4
2
2
0
x
dx
x 1
215/I =
2
0
sin 3x
dx
cos x 1
216/I =
2
2
2
2
0
x
dx
1 x
217/I =
2
2
4
1
1 x
dx
1 x
218/I =
3
7
3 2
0
x
dx
1 x
219/I =
x
ln 2
x
0
1 e
dx
1 e
</div>
<span class='text_page_counter'>(9)</span><div class='page_container' data-page=9>
206/I = 1 2
x 1
dx
x
207/I =
3
4
2
0
sin x
dx
cos x
208/I =
2
2
0
cos x.cos 4x dx
209/I =
1
2x x
0
1
dx
e e
210/I =
e
2
1
e
ln x
dx
(x 1)
211/I =
1
0
1
dx
x 1 x
227/I =
2
6
1 sin 2x cos 2x
dx
cos x sin x
228/I =
x 2
1
2x
0
(1 e )
dx
1 e
229/I =
3
2 3
0
x (1 x) dx
230/I =
3
2
2
0
sin x.cos x
dx
cos x 1
231/I =
1
2
2
0
4x 1
dx
x 3x 2
232*/I =
2
0
x sin x.cos xdx
233/I =
2
0
cos x
dx
cos 2x 7
234/I =
4
2
1
1
dx
x (x 1)
220/I =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 =
2
3
0
x 1
dx
x 1
224/I =
1
2 2x
0
(1 x) .e dx
225/I =
2
2
0
cos x
dx
cos x 1
226/I =
7
3
3
0
x 1
dx
3x 1
<b>.</b>
242/I =
2
0
sin 2x sin x
dx
cos3x 1
243/I =
4
2 2
0
sin 2x
dx
sin x 2cos x
244/I =
2
3
2
2
0
x
dx
1 x
245/I =
2
3
2
2
0
x
dx
1 x
246/I =
2
1
2
2
2
1 x
dx
x
247/I =
2
1
2
0
x
dx
4 x
</div>
<span class='text_page_counter'>(10)</span><div class='page_container' data-page=10>
235/I =
2
2 3
0
sin 2x(1 sin x) dx
236/I =
2
3
0
x 1
dx
3x 2
237/I =
4
2
7
1
dx
x x 9
238/I =
3 4
0
x sin 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
x
0
1 sin x
dx
(1 cos x)e
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 x
e 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 2
0
1
dx
(4 x )
248/I =
2
2
2
3
1
dx
x x 1
249/I =
1
5 3 6
0
x (1 x ) dx
250/I =
2
0
sin x
dx
1 sin x
251/I =
2
0
cos x
dx
7 cos 2x
252/I =
4
2
1
1
dx
(1 x)x
253/I =
2
3
0
x 1
dx
3x 2
254*/I =
3
4
cos x sin x
dx
3 sin 2x
<b> .</b>
267/I =
2
2
0
sin x
dx
cos x 3
268/I =
2
0
sin x
dx
x
269/I =
2
2
0
sin x cos x(1 cos x) dx
270/I =
4 4
4
0
sin x cos x
dx
sin x cos x 1
271/I =
4 4
4
0
sin x cos x
dx
sin x cos x 1
</div>
<span class='text_page_counter'>(11)</span><div class='page_container' data-page=11>
261/I = 0 3
3x
dx
x 2
262*/I =
5
2
5
1
1 x
dx
x(1 x )
263/I =
3
2
0
cos x
dx
1 sin x
264/I =
2
3
6
0
sin x
dx
cos x
265/I =
3
6
0
sin x sin x
dx
cos 2x
265/I =
2
3
1
dx
sin x 1 cos x
266/I =
3
6 2
1
1
dx
x (1 x )
<b>.</b>
281*/I =
2
1
2
0
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 =
3
2
2
1
3x
dx
x 2x 1
285/I =
1
3 2
0
4x 1
dx
x 2x x 2
286/I =
1
2
2
1
2
1
dx
(3 2x) 5 12x 4x
272/I =
2
0
sin x cos x cos x
dx
sin x 2
273/I =
1
1 x
3
a
e
dx
x
274/I =
3 2
1
2
0
x 2x 10x 1
dx
x 2x 9
275/I =
3
1
2 3
0
x
dx
(x 1)
276/I =
1
3
0
3
dx
x 1
277*/I =
4
1
6
0
x 1
dx
x 1
278/I =
1
3
0
x
dx
(2x 1)
279/I =
7
2
1
dx
2 x 1
280/I =
3
2
2
1
2
1
dx
x 1 x
<b>.</b>
295/I =
2
2
2
3
1
dx
x x 1
296/I =
3
7
3 2
0
x
dx
1 x
297*/I =
2
3
1
1
dx
x 1 x
298/I =
3
1
2
0
x
dx
x 1 x
299/I =
1
2
1
1
dx
1 x 1 x
</div>
<span class='text_page_counter'>(12)</span><div class='page_container' data-page=12>
287/I =
1
0
1
dx
x 1 x
288/I =
2
0
cos x
dx
2 cos 2x
289/I =
2
4
cos x sin x
dx
3 sin 2x
290/I =
2
3 3
0
(cos x sin x)dx
291/I =
2
5 4
0
cos x sin xdx
292/I =
2
4 4
0
cos 2x(sin x cos x)dx
293/I =
2
0
1
dx
2 sin x
294/I =
2
0
1
dx
2 cos x
308*/I =
1
2x
1
1
dx
3 e
309*/I =
2
x
sin x
dx
3 1
310*/I =
2
0
sin x
dx
cos x sin x
311/I =
4
2
4 4
0
sin x
dx
cos x sin x
312*/I =
2
2
0
tgx
dx
1 ln (cos x)
300/I =
3
4
6
1
dx
sin x cos x
301/I =
2
0
cos x
dx
cos x 1
302/I =
2
0
cos x
dx
2 cos x
303/I =
2
0
sin x
dx
sin x 2
304/I =
3
2
0
cos x
dx
cos x 1
305/I =
2
0
1
dx
2cos x sin x 3
306/I =
2
2
3
cos x
dx
(1 cos x)
307/I =
4
3
0
tg x dx
321*/I =
4
5
0
tg x dx
322/I =
4
3
6
cotg x dx
323/I =
3
4
4
tg x dx
</div>
<span class='text_page_counter'>(13)</span><div class='page_container' data-page=13>
313*/I =
2
0
sin x
dx
cos x sin x
314*/I =
1
x 2
1
1
dx
(e 1)(x 1)
315*/I =
1
3x 1
0
e dx
316*/I =
2
1
2
0
x
dx
x 4
317*/I =
3
2
4 2
0
cos x
dx
cos 3cos x 3
318*/Tìm x> 0 sao cho
2 t
x
2
0
t e
dt 1
(t 2)
319*/I =
3
2
4
tan x
dx
cos x cos x 1
<sub></sub>
320*/I =
1
2
0
3x 6x 1dx
324*/I =
4
0
1
dx
2 tgx
325/I =
5
2
0
sin x
dx
cos x 1
326/I =
3
2
6
cos 2x
dx
1 cos 2x
327*/I =
4
2
0
t gx 1
( ) dx
tgx 1
328*/I =
1
3
1
2
x
dx
x 1
329*/I =
3 3
2
4
1
x x
dx
x
330/I =
x
ln 3
x x
0
e
dx
(e 1) e 1
331/I =
1
4
e
2
1
e
1
dx
x cos (ln x 1)
333*/I =
4
0
ln(1 tgx)dx
</div>
<!--links-->
