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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