Prepared by Dr. Richard Ng

1. BBMP 1103
Mathematic Management
Exam Preparation Workshop Sept 2011
Part 4 - Integration
Presented By: Dr Richard Ng
26 Nov 2011
2ptg – 4ptg

2. 4. Focus on Integration
Question: 10 (May 2010)
Prepared by Dr Richard Ng (2011) Page 2

3. Suggested Answers:
2
a) (3x x)( x 1).dx (3x 3 3x 2 x2 x).dx
(3x 3 2x 2 x).dx
3x 4 2x3 x2
c
4 3 2
x5 x3 x5 x3
b) 5
.dx 5 5
.dx
x x x
1 x 2 .dx
1
x
x c
1
1
x c
x
Prepared by Dr Richard Ng (2011) Page 3

4. Question: 11 (Jan 2010)
Determine the following:
1 (4 marks)
a) 1 .dx
x3
b) x x3 2 .dx (4 marks)
3
c) (4 x 3 2).dx (4 marks)
2
Prepared by Dr Richard Ng (2011) Page 4

5. Suggested Answers:
1 3
a) 3
1 .dx (x 1).dx
x
2
x
x c
2
1
2
x c
2x
1
b) x x3 2 .dx (x 2 ) x3 2 .dx
7 1
x2 2x 2 .dx
Prepared by Dr Richard Ng (2011) Page 5

6. 7 1
x2 2x 2 .dx
9 3
x2 x2
2 c
9 3
2 2
9 3
2 4
x2 x2 c
9 3
Prepared by Dr Richard Ng (2011) Page 6

7. 3
4
3 4x
c) (4 x 3 2).dx 2x
2 4
2
4 3
x 2x 2
(3) 4 2(3) (2) 4 2(2)
81 6 16 4
87 20
57
Prepared by Dr Richard Ng (2011) Page 7

8. End of
Part 4