Mathematica: NIntegrate data points

In summary, Niles has a set of data points in units of (time, voltage) that form a Gaussian when plotted. They are looking to normalize the data set by finding a factor C to multiply onto the voltage data to make the area 1. They are wondering if there is a way to numerically integrate the data points in Mathematica. An expert suggests using the Apply or Plus functions, or fitting the data to a Gaussian and then integrating it. Niles agrees that integrating the data is overkill and decides to use the first suggestion.
  • #1
Niles
1,866
0
Hi

I have a set of data points in units of (time, voltage), and they have the form of a Gaussian when I plot it. I would like to normalize my data set, i.e. find a factor C that I multiply on to the voltage-data such that the area is 1.

However, is there a way to numerically integrate data points in Mathematica?


Niles.
 
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  • #2
Integration is probably overkill. I would just use:

Apply[Plus,data]

or equivalently:

Plus@@data

If you really want to integrate it then you need to construct an interpolating function object, specify the order of the interpolation and then integrate that. Alternatively, you could fit the data to a Gaussian and then use the integral of the fitted Gaussian.
 
Last edited:
  • #3
Thanks. Yeah, I think integrating it is overkill. Your first suggestion works!Niles.
 

Related to Mathematica: NIntegrate data points

1. What is Mathematica?

Mathematica is a powerful software program used for mathematical and scientific computations, data analysis, and visualization. It is widely used by scientists, engineers, and researchers in various fields.

2. What is NIntegrate in Mathematica?

NIntegrate is a function in Mathematica used for numerical integration. It allows users to integrate functions or data points numerically, without needing an analytical expression for the function.

3. How do I use NIntegrate to integrate data points in Mathematica?

To use NIntegrate in Mathematica, you need to first input the data points as a list of {x,y} pairs. Then, you can use the NIntegrate function with the data points as the first argument and specify the integration range and any other desired options.

4. Can NIntegrate handle data points with errors or uncertainties?

Yes, NIntegrate has options to handle data points with errors or uncertainties. The "Method" option allows you to choose from various numerical integration methods that can handle noisy data. Additionally, the "PrecisionGoal" and "AccuracyGoal" options can be used to control the accuracy of the integration.

5. How can I visualize the results of NIntegrate in Mathematica?

You can use the Plot function in Mathematica to visualize the results of NIntegrate. You can plot the integrated function or data points against the integration range, or you can use the ListPlot function to directly plot the data points used in the integration.

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