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how to integrate a function whose values are represented by a set of data points at time t instead of continuous function of time t

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I have a 't' vector(161 elements) from 0 secs to 4secs. By default Matlab has broken it to be :
0
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0001
0.0001
0.0001
0.0002
0.0004
0.0005
0.0007
0.0009
0.0018
0.0027
0.0036
0.0045
0.0090
0.0135
0.0179
0.0224
0.0335
0.0446
0.0557
0.0667
0.0796
0.0924
0.1053
0.1181
0.1344
0.1508
0.1671
0.1834
0.1978
0.2122
0.2265
0.2409
0.2532
0.2654
0.2777
0.2900
0.3018
0.3136
0.3254
0.3372
0.3480
0.3588
0.3697
0.3805
0.3934
0.4063
0.4192
0.4321
0.4483
0.4646
0.4809
0.4971
0.5115
0.5259
0.5403
0.5546
0.5673
0.5799
0.5926
0.6052
0.6184
0.6315
0.6446
0.6577
0.6683
0.6790
0.6897
0.7003
0.7136
0.7270
0.7403
0.7536
0.7707
0.7877
0.8048
0.8218
0.8366
0.8514
0.8662
0.8810
0.8958
0.9106
0.9254
0.9402
0.9562
0.9722
0.9883
1.0043
1.0228
1.0413
1.0598
1.0783
1.1024
1.1265
1.1506
1.1747
1.2055
1.2362
1.2670
1.2977
1.3256
1.3535
1.3814
1.4093
1.4471
1.4848
1.5226
1.5603
1.6153
1.6704
1.7254
1.7804
1.8323
1.8842
1.9360
1.9879
2.0489
2.1099
2.1709
2.2319
2.2930
2.3540
2.4150
2.4760
2.5390
2.6020
2.6650
2.7280
2.7782
2.8283
2.8784
2.9286
2.9787
3.0288
3.0790
3.1291
3.1933
3.2574
3.3216
3.3858
3.4500
3.5141
3.5783
3.6425
3.6983
3.7541
3.8099
3.8657
3.8993
3.9328
3.9664
4.0000
Now I have a function whose values I know at all these 161 time instants. But,how can I integrate that function in time domain. I guess I cannot use the existing Matlab commands like 'int' etc. Any suggestions?

Accepted Answer

Star Strider
Star Strider on 22 Mar 2014
My suggestion would be trapz or cumtrapz.
The links to cumtrapz and related functions are at the end of the page.

More Answers (1)

Roger Stafford
Roger Stafford on 22 Mar 2014
"I guess I cannot use the existing Matlab commands like 'int' etc. Any suggestions?" That is correct. You must use a function such as 'trapz' which accepts a fixed set of data points rather than a function. Besides your 161-element vector 't' which is to be the variable of integration, you need a vector of your corresponding function of 't' which is to be your integrand and which should also have the same number of elements, 161. Call this integrand vector 'd' (for data.) Then your call would be:
I = trapz(t,d);
You should read the documentation for 'trapz' at
http://www.mathworks.com/help/matlab/ref/trapz.html
In particular, read the section under the title "Integrate Matrix with Nonuniform Spacing" since I see your 't' vector has non-uniform spacing. The 'trapz' routine will nevertheless give you an accurate integral evaluation since your consecutive 't' values are all quite close together.
You should know that there are alternative integration functions in the File Exchange that handle such discrete data with higher order polynomial approximations. If your integrand function is well-behaved, these are capable of higher accuracy for a given discrete set than with the above trapezoidal technique.

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