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Composite Trapezoidal Error Bound

Bound integration error using a second-derivative bound and panel count.

Math workspace● Runs in your browser
01 Your input
02 Your result
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FormulaError Bound = (b-a)**3*M/(12*n**2); Step = (b-a)/n
Sources and model references

Made for real tasks

  • Bound integration error using a second-derivative bound and panel count.
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Worked example

Inputs

Integration start
0 number
Integration end
1 number
Maximum absolute second derivative
2 number
Equal panels
10 count

Expected results

Error Bound
0.001666666667 number
Step
0.1 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 integration start, integration end, maximum absolute second derivative, equal panels.
  2. Use the displayed units and confirm the model assumptions.
  3. Calculate and compare the outputs against your input scenario.

Try this example

{
  "a": 0,
  "b": 1,
  "M": 2,
  "n": 10
}

Accuracy and scope

M must bound the absolute second derivative over the entire interval; this does not estimate the integral itself.

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.