SAMPLE 1 & 2 (ASSESSMENT MAT238)

ONLINE ASSESSMENT 2/MAT238/JAN 2021 (ODL)

UNIVERSITI TEKNOLOGI
MARA PAHANG

MAT238
ONLINE ASSESSMENT 2
3:00 pm – 5:00 pm (2 Hours)
(including uploading your answer in google classroom)

Name : ________________________________________________
UiTM ID : ________________________________________________
Group : ________________________________________________
Lecturer : ________________________________________________

Instructions to candidates

• Answer ALL Questions.
• You are advised to take 1.25 hours (75 minutes) to complete a written exam and 45

minutes to print (if necessary), save in pdf format and upload your answers.
• This is an Open Book Test, but not an Open Discussion Test. So you are not allowed to

share your answers with others. Upload all your answers in one file in pdf format in folder

‘ASSESSMENT 2 MAT238’ in google classroom

• Save your file name as (example)
1. Ahmad Bin Husin(matrix number) (AS1203A)

Your name Matrix.No Your group

Number
Your queue number in SIMNS umber

ASSESSMENT 2 (PLO1)

QUIZ 3 TEST 2 (25 marks)
(6 marks)
Q1 Q2 Q3
(8 m) (8 m) (9 m)



6 25

ONLINE ASSESSMENT 2/MAT238/JAN 2021 (ODL)

QUIZ 3 (6 marks)



Use Integration by parts to solve ∫( 7 + 1) cos 3 . (6 marks)



TEST 2 (25 marks)



7

1. Use integration by parts to solve K √ + 2 . (8 marks)

O



2. By using suitable trigonometric substitution, evaluate

U : 7 = O\]^_ 7`a
7

K 7 . (8 marks)
b49 − 7



3. Evaluate the integral of the following improper rational function.



K i + j + + 2
j − 7

(9 marks)






END OF QUESTION PAPER

ALL THE BEST!!!

1

ONLINE ASSESSMENT 2/MAT238/JAN 2021 (ODL)

APPENDIX 1 (1)

TABLE OF INTEGRALS

ì(ax + b)n+1 + C; n ¹ -1
ïï | +C; n = -1
ò1. (ax + b)n dx = í 1 a(n + 1)
ï a ln | ax +
îï b

ò2. 1 dx = ln | x | +C
x

ò3. sin (ax) dx = - 1 cos (ax) + C
a

ò4. cos (ax) dx = 1 sin(ax) + C
a

ò5. sec 2 (ax) dx = 1 tan(ax) + C
a

ò6. sec (ax) dx = 1 ln | sec (ax) + tan(ax) | +C
a

ò7. sec (ax) tan (ax) dx = 1 sec (ax) + C
a

ò8. sinh(ax) dx = 1 cosh (ax) + C
a

ò9. cosh (ax) dx = 1 sinh(ax) + C
a

ò10. sec h2 (ax) dx = 1 tanh (ax) + C
a

ò11. csc h2 (ax)dx = - 1 coth(ax) + C
a

ò12. sec h(ax) tanh(ax)dx = - 1 sec h(ax) + C
a

ò13. csc h (ax) coth(ax) dx = - 1 csc h(ax) + C
a

ò14. 1 dx = sin-1 çæ x ÷ö + C
a2 - x2 è a ø

2

ONLINE ASSESSMENT 2/MAT238/JAN 2021 (ODL)

APPENDIX 1 (2)

ò15. a2 1 x2 dx = 1 tan-1 æç x ÷ö +C
+ a è a ø

ò16. 1 dx = 1 sec -1 æç x ÷ö +C
x2 - a2 a è a ø
x

ò17. 1 dx = sinh-1 çæ x ÷ö + C = ln | x + a2 + x2 | +C
a2 + x2 è a ø

ò18. 1 dx = cosh-1 æç x ö÷ + C = ln | x + x2 - a2 | + C, if x > a
x2 - a2 è a ø

ò19. a2 1 dx = 1 ln x+a + C = ì 1 tanh -1 çæ x ö÷ + C, if | x |< a
- x2 2a x-a ïï coth -1 è ø + C, if | x |> a
í a æç a ÷ö
ï 1 è x ø
ïî
a a

ò20. 1 dx = - 1 sec h-1 x +C=- 1 ln a+ a2 - x2 + C, if 0 < x < a
a2 - x2 a a a x
x

ò21. 1 dx = - 1 csc h-1 x +C=- 1 ln a+ a2 + x2 + C, if x ¹ 0
a2 + x2 a a a x
x

TRIGONOMETRIC IDENTITIES

1. sin2 x + cos2 x = 1
2. sin2x = 2sin x cos x
3. cos 2x = cos2 x - sin2 x

HYPERBOLIC FUNCTIONS

1. sinh x = ex - e-x
2

2. cosh x = ex + e-x
2

3. cosh 2 x - sinh 2 x = 1

3

ANSWERS

QUIZ 3

∫( 2 + 1) 3 = 1 ( 2 + 1) 3 + 22 3 +
3 9 3 − 27

TEST 2/Q1

∫ √ +2 = 1 ( + 2) − 1 ( + 2) + | + 2| +
2 2

2

∫ √ + 2 = 0.6247

1

TEST 2/Q2

2 = 2 −1 3 − √4 − 9 2 +
∫ 9 () 6

√49 − 2 2

TEST 2/Q3

4 + 3 + + 2 2 − 3 + 2 + 5 | − 1| +
∫ 3 − 2 = 2 + 2



ONLINE ASSESSMENT 2/MAT238/JUN 2021 (ODL)

UNIVERSITI TEKNOLOGI
MARA PAHANG

MAT238
ONLINE ASSESSMENT 2

9:00 pm – 11:00 pm
(2 Hours)

(including uploading your answer in google classroom)

Name :
UiTM ID :
Group :
Lecturer :

Instructions to candidates

• Answer ALL Questions.
• You are advised to take 1.25 hours (75 minutes) to complete a written exam and 45

minutes to print (if necessary), save in pdf format and upload your answers.
• This is an Open Book Test, but not an Open Discussion Test. So you are not allowed to

share your answers with others. Upload all your answers in one file in pdf format in folder
‘ASSESSMENT 2 MAT238’ in google classroom
• Save your file name as (example)
1. Ahmad Bin Husin (matrix number) (AS1203A)

Your name Matrix.No Your group

Your queue number in SIMS

ASSESSMENT 2 (PLO1)

PART A PART B (25 marks)
(6 marks)
Q1 Q2 Q3

(8 m) (8 m) (9 m)

6 25

ONLINE ASSESSMENT 2/MAT238/JUN 2021 (ODL)

PART A (6 marks) (6 marks)
Use integration by parts to solve ∫( 2 − 3) 3

Ans :

PART B (25 marks)

1. Use integration by parts to solve ∫ 2 √ (8 marks)

Ans :

2. Use trigonometric substitution = 4 , to evaluate ∫ 4 .

√16 − 2

(8 marks)

Ans :

3. Evaluate the integral of the following improper rational function.

5 + 2 4 + 3 + + 5
∫ 3 + 2

(9 marks)

Ans :

END OF QUESTION PAPER
ALL THE BEST!!!

ONLINE ASSESSMENT 2/MAT238/JUN 2021 (ODL)

APPENDIX 1 (1)

TABLE OF INTEGRALS

(ax + b)n+1 + C; n  −1
 n = −1
1. (ax + b)n dx =  a(n + 1)

 1 ln | ax + b | +C;
 a

2. 1 dx = ln | x | +C
x

3. sin(ax)dx = − 1 cos(ax) + C
a

4. cos(ax) dx = 1 sin(ax) + C
a

5. sec 2 (ax)dx = 1 tan(ax) + C
a

6. sec (ax)dx = 1 ln | sec (ax) + tan(ax) | +C
a

7. sec (ax) tan(ax)dx = 1 sec (ax) + C
a

8. sinh (ax) dx = 1 cosh(ax) + C
a

9. cosh(ax)dx = 1 sinh (ax) + C
a

10. sec h2 (ax)dx = 1 tanh (ax) + C
a

11. csc h2 (ax)dx = − 1 coth(ax) + C
a

12. sec h(ax) tanh (ax)dx = − 1 sec h(ax) + C
a

13. csc h(ax)coth(ax) dx = − 1 csc h(ax) + C
a

14. 1 dx = sin−1  x  + C
a2 − x2 a

ONLINE ASSESSMENT 2/MAT238/JUN 2021 (ODL)

APPENDIX 1 (2)

15. a2 1 x2 dx = 1 tan−1  x  +C
+ a  a 

16. 1 dx = 1 sec −1  x  + C
x x2 − a2 a a

17. 1 dx = sinh−1  x  + C =ln | x + a2 + x2 | + C
a2 + x2 a

18. 1 dx = cosh−1  x  + C = ln | x + x2 − a2 | + C, if x  a
x2 − a2 a

19. a2 1 dx = 1 ln x+a + C =  1 tanh −1  x  + C, if | x | a
− x2 2a x−a  a coth−1  a  + C, if | x | a
 1  x 

 a  a 

20. 1 dx = − 1 sec h−1 x + C = − 1 ln a + a2 − x2 + C, if 0  x  aa
x a2 − x2 aa x

21. 1 dx = − 1 csc h−1 x + C = − 1 ln a + a2 + x2 + C, if x  0aaa x
x a2 + x2

TRIGONOMETRIC IDENTITIES
1. sin2 x + cos2 x = 1
2. sin 2x = 2 sin x cos x
3. cos 2x = cos2 x − sin2 x

HYPERBOLIC FUNCTIONS
1. sinh x = e x − e −x
2
2. cosh x = ex + e−x
2
3. cosh2 x − sinh2 x = 1