SỞ GIÁO DỤC & ĐÀO TẠO CHƯƠNG 3 NGUYÊN HÀM –TÍCH PHÂN ...
[Pages:11]S GI?O DC & ?O TO TRNG THPT..........
CHNG 3 NGUY?N H?M ?T?CH PH?N
T?n b?i: B?I TP NGUY?N H?M (99 c?u trc nghim)
M? thi 134
H, t?n th? sinh:..................................................................... Lp: .............................
C?u 1: Trong c?c h?m s sau ?y , h?m s n?o l? nguy?n h?m ca f (x) 4 1 5 1 3x 2 x
A. 4 ln 1 3x 5x 3
B. 4 ln 1 3x x 5x 3
C. 4 ln 1 3x x 3
D. 4 ln 1 3x 3
C?u
2: Nguy?n h?m ca h?m s:
J
1 x
x
dx
l?:
A. F(x) = ln x x2 C
C. F(x) = ln x 1 x2 C
2 C?u 3: Chn khng nh sai?
A. sin xdx cos x C
1
C.
sin2
dx x
cot x C
C?u 4: Mt nguy?n h?m ca h?m s y sin3 x.cos x l?:
A. Fx sin4 x 1
4
C. Fx cos2 x cos4 x
2
4
C?u 5: Nguy?n h?m ca h?m s: y =
1 l?:
3 1 4x 10
B. F(x) = ln x 1 x2 C 2
D. F(x) = ln x x2 C
B.
ln xdx
1 x
C
D. 2xdx x2 C
B. Fx sin4 x cos2 x
42
D. Fx cos2 x cos4 x
2
4
A.
3
1
4x
7 3
C
7
B.
12
1
4x
7 3
C
7
C.
3
7
1 4x 3
C
28
D.
3
7
1 4x 3
C
28
C?u 6: T?nh (3cos x 3x )dx , kt qu l?:
A. 3sin x 3x C ln 3
B. 3sin x 3x C ln 3
C. 3sin x 3x C ln 3
C?u 7: Mt nguy?n h?m ca h?m s: y x3 l?: 2 x2
A. x 2 x2
B. 1 x2 2 x2 3
C. 1 x2 4 2 x2 3
D. 3sin x 3x C ln 3
D. 1 x2 4 2 x2 3
C?u 8: T?m x cos 2xdx l?:
A. 1 x sin 2x 1 cos 2x C
2
4
C. x2 sin 2x C 4
B. 1 x sin 2x 1 cos 2x C
2
2
D. sin 2x C
C?u 9: Mt nguy?n h?m ca h?m s f (x) 2sin 3x.cos3x l?
Trang 1/11 - M? thi 134
A. cos3x.sin 3x
B. 1 cos 2x 4
C. 1 sin 2x 4
D. 1 cos 6x 6
C?u 10: T?m (cos 6x cos 4x)dx l?:
A. 6sin 6x 5sin 4x C
C. 1 sin 6x 1 sin 4x C
6
4
B. 1 sin 6x 1 sin 4x C
6
4
D. 6sin 6x sin 4x C
C?u
11:
T?m
mt
nguy?n
h?m
Fx
ca
h?m
s
f x ax
b x2
x 0 , bit rng F1 1, F1 4 ,
f 1 0 . Fx l? biu thc n?o sau ?y
A. Fx x2 1 4
x
C. Fx x2 1 5
2 x2
B. Fx x2 1 2
x
D. Fx x2 1 7
2 x2
C?u 12: Mt nguy?n h?m ca h?m s: f (x) x sin 1 x2 l?:
A. F(x) 1 x2 cos 1 x2 sin 1 x2
B. F(x) 1 x2 cos 1 x2 sin 1 x2
C. F(x) 1 x2 cos 1 x2 sin 1 x2
D. F(x) 1 x2 cos 1 x2 sin 1 x2
C?u 13: Nu f (x)dx ex sin 2x C th? f (x) bng
A. ex cos 2x
B. ex cos 2x
C. ex 1 cos 2x 2
D. ex 2cos 2x
C?u 14: X?c nh a, b, c sao cho g(x) (ax2 bx c) 2x -3 l? mt nguy?n h?m ca h?m s
f (x) 20x2 - 30x 7 2x -3
trong khong
3 2
;
A. a 4, b 2, c 2
B. a 1, b 2, c 4
C. a 2, b 1, c 4
D. a 4, b 2, c 1
C?u
15:
T?nh
nguy?n
h?m
1 dx 1 2x
ta
c
kt
qu
sau:
A. 1 ln 1 2x C 2
B.
2 (1 2x)2
C
C. ln 1 2x C
D. 2ln 1 2x C
C?u 16: Mt nguy?n h?m ca h?m s: y = cos5x l?:
A. sin5x + C
B. cos5x + C
C. 1 sin 5x + C 5
D. 1 sin 6x + C 6
C?u 17: Mt nguy?n h?m ca h?m s: I sin4 x cos xdx l?:
sin5 x
A. I
C
5
cos5 x
B. I
C
5
sin5 x
C. I
C
5
D. I sin5 x C
C?u 18: Nguy?n h?m ca h?m s xex2dx l?
ex2 A. C
2
B. ex2 C
C. xex2 C
D. x ex2
C?u
19:
Nguy?n
h?m
ca
h?m
s
f (x)
2ex
1 cos2
x
l?:
A. 2ex + tanx + C
B. ex + tanx + C
C. Kt qu kh?c
D. ex(2x -
e x cos2
x
)
C?u 20: Trong c?c h?m s sau ?y , h?m s n?o l? nguy?n h?m ca f (x) sin 2x
Trang 2/11 - M? thi 134
A. 2cos 2x
B. 2cos 2x
C. 1 cos 2x 2
D. 1 cos 2x 2
C?u 21: Kt qu n?o sai trong c?c kt qu sau:
A. tan2 xdx tan x x C
C.
x2 1 x2 dx
1 ln 2
x 1 x 1
xC
B.
x4
x4 x3
2 dx
ln
x
1 4x4
C
2x1 5x1
1
1
D.
10x dx 5.2x.ln 2 5x.ln 5 C
C?u 22: Nguy?n h?m ca h?m s: y = cos2x.sinx l?:
A. 1 cos3 x C 3
B. cos3 x C
C. 1 cos3 x C 3
D. 1 sin3 x C 3
C?u 23: T?nh sin(3x 1)dx , kt qu l?:
A. Kt qu kh?c
B. 1 cos(3x 1) C 3
C. 1 cos(3x 1) C 3
D. cos(3x 1) C
C?u 24: H nguy?n h?m ca f (x) x2 2x 1 l? A. F(x) 1 x3 2 x C 3 C. F(x) 1 x3 x2 x C 3
B. F(x) 2x 2 C D. F(x) 1 x3 2x2 x C
3
C?u 25: H?m s Fx ex tan x C l? nguy?n h?m ca h?m s f (x) n?o?
A.
f (x)
ex
1 sin2
x
B.
f (x)
ex
1 cos2
x
C.
f (x)
ex
1 sin2
x
C?u 26: C?ng thc nguy?n h?m n?o sau ?y kh?ng ?ng?
A.
1dx x
ln
x
C
C.
1
cos2
dx x
tan x C
B. xdx x1 C ( 1)
1
D. axdx ax C (0 a 1)
ln a
D. Kt qu kh?c
C?u 27: Trong c?c h?m s sau ?y , h?m s n?o l? nguy?n h?m ca f (x) 1 2x 2016
A. 1 ln 2x 2016 2
B. 2 ln 2x 2016
C. 1 ln 2x 2016 2
D. ln 2x 2016
C?u
28:
Nguy?n
h?m
Fx
ca h?m s
f x
2x4 3 x2
A. Fx 2x3 3 C
3x
C. Fx 3x3 3 C
x
x 0 l?
B. Fx x3 3 C
3x
D. Fx 2x3 3 C
3x
C?u 29: Trong c?c h?m s sau ?y , h?m s n?o l? nguy?n h?m ca f (x) ex cos x
A. ex sin x
B. ex sin x
C. ex sin x
D. ex sin x
C?u 30: H?m s n?o sau ?y kh?ng phi l? nguy?n h?m ca h?m s f (x) x(2 x) (x 1)2
x2 x 1 A.
x 1
x2 x 1 B.
x 1
x2 x 1 C.
x 1
x2 D.
x 1
C?u 31: H?m s n?o l? mt nguy?n h?m ca sin2x
A. sin2 x
B. 2cos2x
C. -2cos2x
D. 2sinx
dx
C?u 32: T?m x2 3x 2 l?:
Trang 3/11 - M? thi 134
A. ln x 2 C x 1
C. ln x 1 C x2
C?u 33: Trong c?c mnh sau, t?m mnh sai
A. f (x) g(x)dx f (x)dx g(x)dx
C. f (x).g(x)dx f (x)dx. g(x)dx
C?u
34:
T?m
dx 3x 1
ta
c
A. ln 3x 1 C
B.
3
3x 12
C
B. ln 1 ln 1 C x 2 x 1
D. ln(x 2)(x 1) C
B. kf (x)dx k f (x)dx (k l? hng s) D. f '(x)f 2 (x)dx f 3(x) C
3
C. ln 3x 1 C
D. 1 ln 3x 1 C 3
C?u
35:
Trong
c?c
h?m
s
sau
?y
,
h?m
s
n?o
l?
nguy?n
h?m
ca
f (x)
1 cos2 (2x 1)
A. 1 co t(2x 1) 2
B. 1 tan(2x 1) 2
1 C. sin2 (2x 1)
1 D. sin2 (2x 1)
C?u 36: Nguy?n h?m ca h?m s: I (x2 3x 1)dx l?:
A. F(x) 1 x3 3 x2 C 32
B. F(x) x3 3 x2 1 x C 22
C. F(x) 1 x3 3 x2 x C 32
D. F(x) 1 x3 3 x2 x C 32
C?u
37:
Nguy?n
h?m
Fx
ca
h?m
s
f
x
x 13
x3
x 0 l?
A.
Fx
x 3ln
x
3 x
1 2x2
C
B.
Fx
x 3ln
x
3 x
1 2x2
C
C.
Fx
x 3ln
x
3 x
1 2x2
C
D.
Fx
x 3ln
x
3 x
1 2x2
C
C?u 38: H?m s Fx ex2 l? nguy?n h?m ca h?m s
A. f x 2x.ex2
B. f x e2x
C. f x ex2
2x
D. f x x2.ex2 1
C?u 39: Nguy?n h?m ca h?m s f(x) = ex (2 ex ) l?:
A. 2ex x C
B. 2ex x C
C. 2ex 2x C
D. ex ex C
C?u 40: Nguy?n h?m F(x) ca h?m s f (x) 4x3 3x2 2 tr?n R tho m?n iu kin F(1) 3 l?
A. x4 x3 2x 4
B. x4 x3 2x 3
C. x4 x3 2x 4
D. x4 x3 2x 3
C?u 41: H?m s n?o di ?y kh?ng
l? nguy?n h?m ca h?m s
f x
x2 x x 12
A. x2 x 1 x 1
B. x2 x 1 x 1
C. x2 x 1 x 1
x2 D.
x 1
C?u 42: Trong c?c h?m s sau ?y , h?m s n?o l? nguy?n h?m ca f (x) x3 3x2 2x 1
A. 1 x4 x3 x2 4
B. 3x2 6x 2
C. 3x2 6x 2
D. 1 x4 x3 x2 x 4
C?u 43: Nguy?n h?m ca h?m s f (x) 1 x x2 l?
A. 1 2x C
B. x2 x3 C 23
C. x x2 x3 C 23
D. x x2 x3 C
Trang 4/11 - M? thi 134
C?u 44: Mt nguy?n h?m ca h?m s: y = cos5x.cosx l?:
A.
1 2
1 6
sin
6x
1 4
sin
4x
B. sin6x
C. cos6x
D.
1 2
sin 6x 6
sin 4x 4
C?u 45: Nguy?n h?m ca h?m s f(x) = 2sin3xcos2x
A. 1 cos 5x cos x C 5
B. 1 cos 5x cos x C 5
C. 5cos5x cos x C
D. Kt qu kh?c
C?u 46: T?m h?m s f(x) bit rng f'(x) = 2x + 1 v? f(1) = 5
A. x2 + x + 3
B. x2 + x - 3
C. x2 + x
D. Kt qu kh?c
C?u 47: Mt nguy?n h?m ca h?m s: y = sinx.cosx l?:
A. cos8x + cos2x+C
B. 1 cos 2x +C 4
C. cos x.sin x +C
D. 1 cos 2x +C 2
C?u
48:
T?nh
nguy?n
h?m
1 dx 2x 1
ta
c
kt
qu
sau:
A. ln 2x 1 C
B. ln 2x 1 C
C. 1 ln 2x 1 C 2
D. 1 ln 2x 1 C 2
C?u 49: T?nh tan2 xdx , kt qu l?:
A. x tan x C
B. x tan x C
C. x tan x C
D. 1 tan3 x C 3
C?u 50: T?m nguy?n h?m (1 sin x)2dx
A. 2 x 2cos x 1 sin 2x C
3
4
C. 2 x 2cos x 1 sin 2x C
3
4
B. 2 x 2cos 2x 1 sin 2x C
3
4
D. 2 x 2cos x 1 sin 2x C
3
4
C?u 51: Trong c?c mnh sau ?y, mnh n?o sai ?
(I)
sin
x
sin
3xdx
1 4
(sin
2x
-
1 2
sin
4x)
C
(II) tan2 xdx 1 tan3 x C
3
(III)
x2
x 1 2x
3
dx
1 2
ln(x 2
2x
3)
C
A. Ch (II) v? (III)
B. Ch (II)
C. Ch (I) v? (II)
D. Ch (III)
C?u 52: T?nh: P x.exdx
A. P x.ex ex C B. P x.ex ex C
C. P x.ex C
D. P ex C
C?u 53: La chn phng ?n ?ng:
A. cot xdx ln sin x C
C.
1 dx x2
1 x
C
B. sin xdx cos x C D. cos xdx sin x C
C?u 54: Nguy?n h?m ca h?m s f(x) =
2x
3 x2
l? :
A. Kt qu kh?c
B.
x2
3 x2
C
C. x2 3ln x2 C
D. x2 3 C x
C?u 55: Nguy?n h?m ca h?m s f (x) (1 2x)5 l?:
Trang 5/11 - M? thi 134
A. 5(1 2x)4 C
B. 5(1 2x)6 C
C?u 56: Trong c?c h?m s sau: (I) f (x) tan2 x 2
(II)
f (x)
2 cos2
x
C. (1 2x)6 C
D. 1 (1 2x)6 C 2
(III) f (x) tan2 x 1
H?m s n?o c? mt nguy?n h?m l? h?m s g(x) = tanx
A. (I), (II), (III)
B. Ch (II)
C. Ch (II), (III)
11 C?u 57: Nguy?n h?m ca h?m s f (x) x x2 l? :
1 A. lnx - + C
x
1 B. ln|x| + + C
x
C. ln x ln x2 C
D. Ch (III) D. Kt qu kh?c
C?u 58: T?m nguy?n h?m
3
x2
4 x
dx
A. 5 3 x5 4 ln x C 3
C. 3 3 x5 4 ln x C 5
B. 3 3 x5 4 ln x C 5
D. 3 3 x5 4 ln x C 5
C?u 59: T?m h?m s f(x) bit rng f'(x) = 4 x x v? f(4) = 0
A. 8x x x2 40 3 23
B. Kt qu kh?c
C. 8x
x x2 40
3 23
C?u 60: Nguy?n h?m ca h?m s: y =
ex 2 x
l?:
A.
ex 2x ln
2
C
B.
ex (1 ln 2)2x
C
C.
ex x.2x
C
D.
ex ln 2x
2
C
C?u 61: Nguy?n h?m ca h?m s f (x) e2x ex l?:
A. ex (ex x) C
B. 2e2x ex C
C. Kt qu kh?c
D. 8
x x2 40
3 23
D. 1 e2x ex C 2
C?u 62: Mt nguy?n h?m ca h?m s y x 1 x2 l?:
A. Fx x2
2
1 x2
2
C. Fx 1
2
1 x2
3
B. Fx 1
2
1 x2
2
D. Fx 1
3
1 x2
3
C?u 63: Mt nguy?n h?m ca h?m s y 2 ln x l?: x
A. Fx ln2 x
2
B. Fx ln x2
C. Fx ln2 x
D. Fx 2ln2 x
C?u 64: Nguy?n h?m ca h?m s f x cos3x l?:
A. sin 3x C
B. 1 sin 3x C 3
C. 1 sin 3x C 3
D. 3sin 3x C
C?u 65: T?nh: P (2x 5)5dx
(2x 5)6
A. P
C
6
(2x 5)6
B. P
C
2
Trang 6/11 - M? thi 134
C. P (2x 5)6 C . 5
D. P 1 . (2x 5)6 C 26
C?u 66: Nguy?n h?m ca h?m s f (x) (2x 1)3 l?:
A. Kt qu kh?c
B. (2x 1)4 C
C. 1 (2x 1)4 C 2
D. 2(2x 1)4 C
C?u 67: Nguy?n h?m ca h?m s f (x) x l?
A. 1 C 2x
B. 3 x x C 2
C. x C
D. 2 x x C 3
C?u 68: H?m s F(x) ex t anx C l? nguy?n h?m ca h?m s f (x) n?o ?
A.
f (x)
ex
1 sin2
x
B.
f (x)
ex
1 cos2x
C.
f (x)
ex
1 cos2x
D.
f (x)
ex
1 sin2
x
C?u 69: Trong c?c h?m s sau ?y , h?m s n?o l? nguy?n h?m ca f (x) e3x3
A. 3 e3x3
B. -3 e3x3
C. 1 e3x3 3
D. e3x3
C?u 70: Mt nguy?n h?m ca h?m s y 3x.ex2 l?:
A. Fx 3ex2
B. Fx 3 ex2
2
C. F x 3x2 ex2
2
D. F x x2 ex3
2
C?u 71: Mt nguy?n h?m ca h?m s y 2x ex 1 l?:
A. Fx 2ex x 1 x2
B. Fx 2ex x 1 4x2
C. Fx 2ex 1 x 4x2
D. Fx 2ex 1 x x2
C?u 72: T?m (sin x 1)3 cos xdx l?:
A. (cos x 1)4 C 4
B. 4(sin x 1)3 C
C. (sin x 1)4 C 4
D. sin4 x C 4
C?u 73: Mt nguy?n h?m ca h?m s y x sin 2x l?:
A. Fx x cos 2x 1 sin 2x
2
4
C. Fx x cos 2x 1 sin 2x
2
2
B. Fx x cos 2x 1 sin 2x
2
2
D. Fx x cos 2x 1 sin 2x
2
4
C?u 74: Mt nguy?n h?m
ca h?m s
y
ln 2x x2
l?:
A. Fx 1 ln 2x 2
x
C. Fx 1 ln 2x 2
x
B. Fx 1 ln 2x 2
x
D. Fx 1 2 ln 2x
x
C?u 75: T?m h?m s y f (x) bit f (x) (x2 x)(x 1) v? f (0) 3
A. y f (x) 3x2 1 C. y f (x) x4 x2 3
42
B. y f (x) x4 x2 3 42
D. y f (x) x4 x2 3 42
C?u 76: Nguy?n h?m ca h?m s y (t anx cot x)2 l?:
A. Fx 1 (t anx cot x)3 C
3
C.
F
x
2(t
anx
cot
x)(
1 cos2
x
1 sin2
)C x
B. Fx t anx-cot x C D. Fx t anx+cot x C
Trang 7/11 - M? thi 134
1 C?u 77: Nguy?n h?m ca h?m s: y = cos2x sin2 x l?:
A. t anx.cot x C
B. t anx-cot x C C. t anx-cot x C
D. 1 sin x C 22
b C?u 78: T?m h?m s f(x) bit rng f '(x) ax+ x2 , f '(1) 0, f (1) 4, f (1) 2
A. x2 1 5 2 x2
B. x2 1 5 2 x2
C. Kt qu kh?c
D. x2 1 5 2 x2
C?u
79:
Nguy?n
h?m
Fx
ca
h?m
s
f
x
x2
1
2
x
x3 x
A. Fx
3 x2
C
2
C. Fx x3 1 2x C
3x
x 0 l?
B.
Fx
x3 3 x2
2
x
3
C
D. Fx x3 1 2x C
3x
C?u 80: Nguy?n h?m ca h?m s: y = cos2 x l?: 2
A. 1 (x sin x) C 2
B. 1 (1 cosx) C 2
C. 1 cos x C 22
D. 1 sin x C . 22
C?u 81: Mt nguy?n h?m ca h?m s: y = cos x l?: 5sin x 9
A. ln 5sin x 9
B. 1 ln 5sin x 9 5
C. 1 ln 5sin x 9 5
D. 5ln 5sin x 9
C?u 82: Cho f (x) 3x2 2x 3 c? mt nguy?n h?m trit ti?u khi x 1. Nguy?n h?m ? l? kt qu n?o
sau ?y?
A. F(x) x3 x2 3x 2
B. F(x) x3 x2 3x 1
C. F(x) x3 x2 3x 1
D. F(x) x3 x2 3x
C?u 83: Trong c?c h?m s sau: (I) f (x) x2 1 (II) f (x) x2 1 5
(III) f (x)
1 x2 1
(IV) f (x) 1 - 2 x2 1
H?m s n?o c? mt nguy?n h?m l? h?m s F(x) ln x x2 1
A. Ch (I)
B. Ch (III)
C. Ch (II)
D. Ch (III) v? (IV)
C?u 84: Nguy?n h?m ca h?m s f(x) = x2 ? 3x + 1 l?: x
A. x3 3x2 ln x C
x3 3x2 B. ln x C
32
C.
x3 3
3x2 2
1 x2
C
D. x3 3x2 ln x C 32
C?u 85: Nu
f (x) (ax2 bx c)
2x -1
l? mt nguy?n h?m ca h?m s
10x2 - 7x 2 g(x)
tr?n
2x -1
khong
1 2
;
th?
a
+
b
+
c
c?
gi?
tr
l?
A. 3
B. 0
C. 4
D. 2
C?u 86: T?m 2x 15dx ta c
Trang 8/11 - M? thi 134
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