Ngọc huyền lb tinh túy casio buổi 10 casio nguyên hàm tích phân (handout)

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TINH TÚY CASIO
Ngày học ___/___/___

HỆ THỐNG ĐÀO TẠO
TOÁN NGỌC HUYỀN LB
Sưu tầm & biên soạn

TINH TÚY CASIO
BUỔI 10. CASIO NGUYÊN HÀM TÍCH PHÂN


BON
(viết tắt: the Best Or Nothing).
Cơ mong các trị ln khắc cốt
ghi tâm khí chất BONer:

"Nếu tơi quyết làm gì, tơi sẽ làm
nó một cách thật ngoạn mục,
hoặc tơi sẽ khơng làm gì cả”.

1. Bài tốn xác định nguyên hàm của một hàm số
Phân tích: Nếu F  x   C là một họ nguyên hàm của hàm số f  x  , tức là

d
 f  x  dx  F  x   C thì F  x  f  x   f  x   F  x   dx  F  x  x  x
0

0

.

0

 QUICK NOTE

Khi đó





d
F  x
 f  x0   0 .
x  x0
dx

Quy trình bấm máy:
* Bước 1: Nhập vào máy





d
FX
 f X .
xX
dx

* Bước 2: Ấn r, máy hỏi X? Ấn x 0  X  x0  với x 0 là một số tùy ý thỏa mãn điều

kiện.
* Bước 3: Ấn =, máy hiện kết quả. Nếu kết quả bằng 0 thì chọn đáp án tương ứng
với F  X  vừa nhập ở bước 1. Còn nếu kết quả khác 0 thì loại ngay đáp án đó và
thực hiện tương tự với các đáp án cịn lại.

BON 01 Họ nguyên hàm của hàm số f  x   cos x  6x là
A. sin x  3x2  C .

B.  sin x  3x2  C .

C. sin x  6x2  C .

D.  sin x  C .

 LỜI GIẢI
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1

2 x  1  C.

2 x  1  C.

B.

 f  x  dx  3  2x  1

D.

 f  x  dx  2

1

1

2 x  1  C.

2 x  1  C.

 LỜI GIẢI
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BON 03 Tìm nguyên hàm của hàm số f  x  
dx

1

A.

 5x  2  5 ln 5x  2  C .

C.

 5x  2   2 ln 5x  2  C .

dx

1

1
.
5x  2
dx

B.

 5x  2  ln 5x  2  C .

D.

 5x  2  5ln 5x  2  C .

dx

 LỜI GIẢI
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2

TINH TÚY CASIO

 QUICK NOTE

BON 04 Tìm nguyên hàm của hàm số f  x   cos3x .
sin 3x
C .
3

A.  cos3xdx  3 sin 3x  C .

B.  cos 3xdx 

C.  cos3xdx  sin 3x  C .

D.  cos 3xdx  

sin 3x
C .
3

 LỜI GIẢI
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16



C .

16

C .

B. 
D.



1 2
x 7
32



1 2
x 7
32





16

16

C .

C .

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1
.
x

B.

x3
1
 3x  2  C , C 
3
x

D.

x3 3x

 ln x  C , C 
3 ln 3

.
.

 LỜI GIẢI
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

BON 07 Tìm nguyên hàm của hàm số f  x   e x  2017 


2018e  x 
.
x5 

x



2018
C .
x4

B.

 f  x  dx  2017 e

x



504,5
C .
x4

D.

 f  x  dx  2017 e

A.

 f  x  dx  2017 e

C.

 f  x  dx  2017 e

x

x



2018
C .
x4



504,5
C .
x4

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ex 
 là
cos2 x 

1
C .
cos x

D. 2 e x 

1
C .
cos x

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D. F  x   x3  6x2  11x2  6x  C .

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5

TINH TÚY CASIO

 QUICK NOTE

BON 10
A.

C.

Hàm số y 

2x  2
x  2x  5
2

x 1
x2  2 x  5

 C.

có nguyên hàm là
B. 2 x2  2x  5  C.

x2  2x  5
 C.
2

D.

x2  2x  5  C.

 LỜI GIẢI
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BON 11

Họ nguyên hàm của hàm số f  x  







x ln x  x2  1
x2  1



 là


A. F  x   x ln x  x 2  1  C.

B. F  x   ln x  x 2  1  x  C.

C. F  x   ln x2  1  x  C.

D. F  x   x 2  1 ln x  x 2  1  x  C.





 LỜI GIẢI

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6

TINH TÚY CASIO

 QUICK NOTE

BON 12

Hàm số F  x   ln sin x  3cos x là một nguyên hàm của hàm số nào

sau đây?
A. f  x  

cos x  3sin x
.
sin x  3cos x

B. f  x   cos x  3sin x.

C. f  x  

 cos x  3sin x
.
sin x  3cos x

D. f  x  

sin x  3cos x
.
cos x  3sin x

 LỜI GIẢI
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BON 13

 1

Hàm số f  x   cos x 
 x  có nguyên hàm là
 cos x



 x
x2 
A. F  x   sin x 
   C.
 sin x 2 

B. F  x   x 1  sin x   cos x  C.

C. F  x   x 1  sin x   cos x  C.

D. F  x   x 1  sin x   cos x  C.

 LỜI GIẢI
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ln 2 x
 x 2  C.
2

ln 2 x  x 2
 C.
2


x2 
D. F  x   ln x  ln x 
  C.
2ln x 


 LỜI GIẢI
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8

TINH TÚY CASIO

 QUICK NOTE

2. Bài toán xác định nguyên hàm F(x) của hàm số f(x) biết F(x0) = k với k là
một số thực
Quy trình bấm máy:
X

* Bước 1: Nhập vào máy F  X   k   f  X  dx .
x0

* Bước 2: Ấn r, máy hỏi X? Nhập X tùy ý (sao cho thỏa mãn điều kiện đề bài)
* Bước 3: Ấn =, máy hiện kết quả.
* Bước 4: Quan sát kết quả. Nếu kết quả nhận được có ít nhất một giá trị khác 0 thì
loại ngay đáp án tương ứng và kiểm tra các đáp án khác. Còn nếu kết quả luôn cho
giá trị bằng 0 với nhiều giá trị của X thì chọn đáp án tương ứng.

BON 15

Hàm số f  x  có đạo hàm liên tục trên

và: f   x   2e2 x  1,

x, f  0   2 . Hàm f  x  là
A. y  2ex  2x .

B. y  2ex  2 .

C. y  e2 x  x  2 .

D. y  e2 x  x  1 .

 LỜI GIẢI
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B. F  x   e sin x .

C. F  x   ecos x  4.

D. F  x   e cos x .

 LỜI GIẢI
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10

TINH TÚY CASIO

 QUICK NOTE

BON 18

 
Tìm hàm số f  x  biết f   x  sin x  cos x và f    0.
4

A. f  x    cos x  sin x  2.

B. f  x   cos x  sin x 

2
.
2

C. f  x   cos x  sin x  2.

D. f  x   cos x  sin x 

2
.
2

 LỜI GIẢI
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 6.
x1

x2
2
13
x
 .
2
x1 6

B. F  x   x2  x 
D. F  x  

2
13
 .
x1 6

x2
2
x
 6.
2
x1

 LỜI GIẢI
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11

TINH TÚY CASIO

 QUICK NOTE

BON 20 Nguyên hàm F  x  của hàm số f  x   x  sin x thỏa mãn F  0   19 là
x2

.
2

B. F  x    cos x 

x2
 2.
2

x2
 20.
2

D. F  x    cos x 

x2
 20.
2

A. F  x    cos x 
C. F  x   cos x 

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và F    1 là
2
sin x
4

B. cot x  x 2 

2
.
16

D. cot x  x 2 

2
.
16

 LỜI GIẢI
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C. F  x  

1
x
1  tan
2



1
 
thỏa mãn F    3 là
1  sin x
3

B. F  x  
3 3
.
2

D. F  x  

2
x
1  tan
2

 3.

2

 3  6.
x
tan  1
2

 LỜI GIẢI
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BON 23 Một nguyên hàm F  x  của hàm số f  x   sin x 

1
thỏa mãn
cos 2 x


2
là
F  
4 2
A. F  x    cos x  tan x  2  1.

B. F  x   cos x  tan x  2  1.

C. F  x    cos x  tan x  1  2.

D. F  x    cos x  tan x.

 LỜI GIẢI
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sin 3 x
.
3

B. F  x  

x sin 2 x

.
2
4

C. F  x  

x sin 2 x 1

 .
2
4
4

D. F  x  

sin 3 x
2

.
3
12

 LỜI GIẢI
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BON 25 Cho hàm số y  f  x  

1
. Nếu F  x  là nguyên hàm của hàm số
sin 2 x

 
f  x  và đồ thị y  F  x  đi qua điểm M  ; 0  thì F  x  là
6 

A. F  x  

3
 cot x.
3

C. F  x    3  cot x.

B. F  x   

3
 cot x.
3

D. F  x   3  cot x.

 LỜI GIẢI
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* Bước 1: Nhập vào máy

 f  X;M dx  I  M , với biến X và M được nhập từ bàn
i

a

phím máy tính.
* Bước 2: Ấn r, máy hỏi X? Ấn = để bỏ qua (không nhập X). Máy hỏi M? Ta
chọn M tùy ý thỏa mãn giả thiết bài tốn (nếu có).
* Bước 3: Ấn = và quan sát kết quả. Nếu máy hiện kết quả bằng 0 thì chọn đáp
án tương ứng. Nếu máy hiện kết quả khác 0 thì loại đáp án tương ứng và thử tiếp
đối với các đáp án khác.

BON 26 Giá trị của tích phân I 





A. I  2m 4m2  8m  5 .
C. I  4m2  8m  5.

2m

  3x
0

2



 8x  5 dx bằng:


D. I  m  4m



B. I  m 4m2  8m  5 .
2



 8m .

 LỜI GIẢI
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Ib page "Tốn Ngọc Huyền LB" để đăng kí học

15

TINH TÚY CASIO

 QUICK NOTE

BON 27 Tính tích phân I 

m 3



m

A. I 


.
3m

B. I 

dx
,  m  1 . Chọn kết quả đúng.
x  m2
2


.
2m

C. I 


.
6m

D. I 


.
12 m

 LỜI GIẢI
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C. m.

D. 2m.

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 b cos x 1  e  dx là

4

3 x

2

C.

4a
.
b

D.

a
.
b

 LỜI GIẢI
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4. Bài tốn tìm tham số để tích phân bằng một giá trị cho trước
BON 30 Tìm giá trị của a để

a

  2x  1 ln xdx  2ln 2  2 . Chọn đáp án đúng.
1

1

A. a  2.

B. a  2.

C. a  3.

D. a  3.

 LỜI GIẢI
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Ib page "Toán Ngọc Huyền LB" để đăng kí học

17

TINH TÚY CASIO

 QUICK NOTE

BON 31

a

Nếu

  cos x  sin x dx  0, 0  a  2   thì giá trị a

bằng

0

A.


.
4

B.


.
2

C.

3
.
2

D. .

 LỜI GIẢI
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8 1
 ln 5 là
3 3

C. m  ln4.

D. m  ln5.

 LỜI GIẢI
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B. m  4.

C. m  3.

dx  m 

7
m

là

D. m  2.

 LỜI GIẢI
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

2

dx  0 . Khi đó 144m2  1 bằng

C.

1
.
3

D.

2
.
3

 LỜI GIẢI
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Ngọc huyền lb tinh túy casio buổi 10 casio nguyên hàm tích phân (handout)

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