This document is a workshop presentation on the application of integration. It provides sample exam questions and worked out solutions involving calculating costs using integration. For example, one question asks the participant to calculate the increase in cost when the value of x increases from 100 to 150, given the derivative of the cost function C'(x) = 30x. The solution shows integrating C'(x) to find the cost function C(x), and substituting the x values to calculate the increase in cost. A second question similarly calculates the small increase in cost when x increases from 200 to 400.

1. BBMP 1103
Mathematic Management
Exam Preparation Workshop Sept 2011
Part 5 - Application of Integration
Presented By: Dr Richard Ng
26 Nov 2011
2ptg – 4ptg

2. 5. Focus on Application of Integration
Question: 12 (May 2010)
Prepared by Dr Richard Ng (2011) Page 2

3. Suggested Answers:
i) Given C' 30x
Hence, C 30x.dx
x2
30 c
2
15x 2 c
When x = 0, c = 15000
Hence, C 15x 2 15000
Prepared by Dr Richard Ng (2011) Page 3

4. ii) When x = 100:
C 15(100) 2 15000
150000 15000
165000
When x = 150:
C 15(150) 2 15000
15(22500) 15000
352500
Hence, increase in cost = 352500 - 165000 = RM187,500
Prepared by Dr Richard Ng (2011) Page 4

5. Question: 13 (Jan 2010)
Prepared by Dr Richard Ng (2011) Page 5

6. Suggested Answers:
80000
i) Given C '
x2
80000
Hence, C 2
.dx
x
80000x 2 .dx
1
80000x
c
1
80000
c
x
Prepared by Dr Richard Ng (2011) Page 6

7. When x = 0, c = 27000
80000
Hence, C 27000
x
ii) When x = 200
80000
C 27000
(200)
400 27000
26600
Prepared by Dr Richard Ng (2011) Page 7

8. When x = 400
80000
C 27000
(400)
200 27000
26800
Hence, increase in cost = 26800 - 26600 = RM200
Prepared by Dr Richard Ng (2011) Page 8

9. End of
Part 5