Technology for Chapter 5: Simulation Modeling in EXCEL

Using Monte Carlo simulation, find the approximate area under the curve y= cos (x) over the interval .

In EXCEL, we can obtain random numbers by using the commands

=RAND( ) This generates a random number between 0-1

=RANDBETWEEN(a,b) This generates a random number as an integer between integers a and b.

2. Deterministic Models
Area Under the Curve
y=f(x)=cos(x) between [-pi/2,pi/2] and 0 < cos(x) <2

The plot:

The EXCEL Output:

WE will do 100 iterations
Iterations / x / y / cos(x) / Counter / Area=
1 / 0.614429 / 1.540378 / 0.817103 / 0
2 / -0.85002 / 0.441809 / 0.659968 / 1
3 / -0.8188 / 0.765603 / 0.683098 / 0
4 / -0.30872 / 0.252463 / 0.952724 / 1
5 / 0.144953 / 1.165235 / 0.989513 / 0
6 / 1.34791 / 0.78889 / 0.221045 / 0
7 / -0.92075 / 0.80286 / 0.605225 / 0
8 / -0.80346 / 1.549956 / 0.69422 / 0
9 / 1.123038 / 1.599954 / 0.432946 / 0
10 / 0.016517 / 1.309035 / 0.999864 / 0
11 / -0.55727 / 1.323064 / 0.848701 / 0
12 / -0.11547 / 1.867228 / 0.99334 / 0
13 / 0.281017 / 1.933094 / 0.960774 / 0
14 / -0.0893 / 0.202792 / 0.996016 / 1
15 / 0.101115 / 1.375639 / 0.994892 / 0
16 / 0.943464 / 0.436537 / 0.586987 / 1
17 / 0.4383 / 1.708847 / 0.905474 / 0
18 / 0.479334 / 0.722906 / 0.887302 / 1
19 / 0.681015 / 1.342153 / 0.776934 / 0
20 / 1.092832 / 1.13835 / 0.459973 / 0
21 / 1.280599 / 1.720611 / 0.286141 / 0
22 / -1.07154 / 0.638368 / 0.47877 / 0
23 / -1.18037 / 0.496891 / 0.38058 / 0
24 / 0.169521 / 1.172678 / 0.985666 / 0
25 / -0.8702 / 1.412704 / 0.644677 / 0
26 / 0.805563 / 0.66016 / 0.692705 / 1
27 / 0.407147 / 1.159312 / 0.918254 / 0
28 / -1.40656 / 1.726509 / 0.163503 / 0
29 / 0.861091 / 1.93269 / 0.65161 / 0
30 / -1.07828 / 1.01462 / 0.472847 / 0
31 / -0.70854 / 0.842768 / 0.759316 / 0
32 / -0.80858 / 0.607992 / 0.690525 / 1
33 / -1.35813 / 1.164469 / 0.211066 / 0
34 / 0.129367 / 0.022001 / 0.991644 / 1
35 / 0.541742 / 1.843163 / 0.856812 / 0
36 / 1.569562 / 1.972188 / 0.001235 / 0
37 / -0.39275 / 0.626702 / 0.92386 / 1
38 / 0.933381 / 0.615082 / 0.59512 / 0
39 / -1.10147 / 1.641888 / 0.452289 / 0
40 / 1.135168 / 1.931666 / 0.42198 / 0
41 / -0.63194 / 0.469944 / 0.806883 / 1
42 / 1.346449 / 1.809136 / 0.22247 / 0
43 / -0.18473 / 0.601631 / 0.982987 / 1
44 / -1.24099 / 0.301875 / 0.323858 / 1
45 / 1.40858 / 0.296831 / 0.161505 / 0
46 / -0.4021 / 0.152461 / 0.92024 / 1
47 / -0.18665 / 0.809951 / 0.982631 / 1
48 / -1.1329 / 1.506694 / 0.424031 / 0
49 / -0.52515 / 0.820476 / 0.865247 / 1
50 / 1.151625 / 1.995533 / 0.407004 / 0
51 / -0.11583 / 1.142185 / 0.993299 / 0
52 / 0.344953 / 1.62168 / 0.941091 / 0
53 / 0.335369 / 0.057127 / 0.944289 / 1
54 / -0.12774 / 1.939639 / 0.991852 / 0
55 / 0.140517 / 1.858858 / 0.990144 / 0
56 / -1.5645 / 0.57871 / 0.006292 / 0
57 / 1.031425 / 1.198667 / 0.513597 / 0
58 / -0.40539 / 0.409063 / 0.91895 / 1
59 / 0.385851 / 0.695823 / 0.926478 / 1
60 / 0.361118 / 1.329776 / 0.935502 / 0
61 / 0.028197 / 0.616062 / 0.999602 / 1
62 / -0.36456 / 0.92314 / 0.934282 / 1
63 / 1.014951 / 0.54559 / 0.527662 / 0
64 / -1.16692 / 0.213632 / 0.392988 / 1
65 / -0.75591 / 1.921474 / 0.727645 / 0
66 / 0.235928 / 1.5666 / 0.972298 / 0
67 / -0.75303 / 0.662003 / 0.729618 / 1
68 / -0.16025 / 1.214153 / 0.987187 / 0
69 / -0.19885 / 0.431417 / 0.980293 / 1
70 / 1.430908 / 1.812025 / 0.139432 / 0
71 / -0.35336 / 0.431691 / 0.938216 / 1
72 / 0.203093 / 1.674002 / 0.979447 / 0
73 / -0.4178 / 1.232741 / 0.913983 / 0
74 / 1.126729 / 0.850714 / 0.429615 / 0
75 / 1.068207 / 1.438019 / 0.481696 / 0
76 / 1.397421 / 1.362517 / 0.172508 / 0
77 / 1.246464 / 1.104458 / 0.318676 / 0
78 / 0.519294 / 1.306986 / 0.86817 / 0
79 / 0.618243 / 1.98601 / 0.814898 / 0
80 / 1.42582 / 1.456081 / 0.144469 / 0
81 / -0.94829 / 0.444797 / 0.583074 / 1
82 / -0.25549 / 1.500115 / 0.967539 / 0
83 / -0.66453 / 1.732754 / 0.787208 / 0
84 / 1.537315 / 0.217347 / 0.033475 / 0
85 / -0.86081 / 0.110344 / 0.65182 / 1
86 / -0.26018 / 0.149297 / 0.966345 / 1
87 / -0.91526 / 1.432271 / 0.609586 / 0
88 / -1.51533 / 0.725801 / 0.055439 / 0
89 / -0.90347 / 0.121623 / 0.618887 / 1
90 / 0.172927 / 1.646032 / 0.985085 / 0
91 / -1.31661 / 1.009301 / 0.251456 / 0
92 / -1.27197 / 1.8148 / 0.294395 / 0
93 / -0.3552 / 0.288139 / 0.937578 / 1
94 / -0.66336 / 0.583429 / 0.78793 / 1
95 / 0.716202 / 1.341714 / 0.754304 / 0
96 / -1.09445 / 1.065013 / 0.458532 / 0
97 / -1.27475 / 0.084976 / 0.291742 / 1
98 / 1.333781 / 0.829555 / 0.234803 / 0
99 / 0.277686 / 1.530661 / 0.961692 / 0
100 / 0.809884 / 1.129383 / 0.689583 / 0
31