How to do numerical integration from data set?

Questions
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1

How to do numerical integration from a data set?

2

Look up Interpolation and NIntegrate. Here is an example:

fun = Interpolation[{{0, 0}, {0.1, .3}, {0.5, .6}, {1, -.2}, {2, 3}}]

NIntegrate[fun[x], {x, 0, 2}]
3

Strongly related SE thread: How to integrate functions of linearly interpolated data?

4

When I integrate using the definite integral symbol in conjunction with the N symbol I get a small complex numerical in addition to the correct answer. What does that mean and what action is necessary.
Luke

5

Use the Chop command.

http://reference.wolfram.com/mathematica/ref/Chop.html

Or you can use Re to get the real part of the complex number.

6

What it means is that during the calculation there were two complex intermediate results whose imaginary components almost cancelled.

If the calculation were done with exact numbers (Integers and Rationals), the imaginary components would have exactly cancelled.

7

How do I import excell data to mathematica and inverse

8

Please see these examples in the documentation.


http://reference.wolfram.com/mathematica/howto/ImportASpreadsheet.html
http://reference.wolfram.com/mathematica/howto/ExportASpreadsheet.html