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THE FEUTEX TOOLKIT

Boole Five-Point Integration

Integrate a smooth function using five equally spaced samples and Boole weights.

Math workspace● Runs in your browser
01 Your input
02 Your result
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FormulaIntegral = 2*h*(7*y0+32*y1+12*y2+32*y3+7*y4)/45
Sources and model references

Made for real tasks

  • Integrate a smooth function using five equally spaced samples and Boole weights.
Explore step-by-step workflows →

Worked example

Inputs

Sample spacing
1 number
Sample 0
0 number
Sample 1
1 number
Sample 2
16 number
Sample 3
81 number
Sample 4
256 number

Expected results

Integral
204.8 number

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

  1. Enter sample spacing, sample 0, sample 1, sample 2, sample 3, sample 4.
  2. Use the displayed units and confirm the model assumptions.
  3. Calculate and compare the outputs against your input scenario.

Try this example

{
  "h": 1,
  "y0": 0,
  "y1": 1,
  "y2": 16,
  "y3": 81,
  "y4": 256
}

Accuracy and scope

Closed five-point Newton–Cotes rule. Equal spacing is mandatory; exact through polynomial degree five.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.