Integration Methods Comparison

Evaluate integral value using Riemann and Lebesgue integration methods for Gaussian PDF.

Start of Integration Range (a):

End of Integration Range (b):

Number of Points (Riemann):

Number of Levels (Lebesgue):

Riemann Integration Results

Integral Value: 0.000000

Sample Mean: 0.000000

Sample Variance: 1.000000

Lebesgue Integration Results

Integral Value: 0.000000

Sample Mean: 0.000000

Sample Variance: 1.000000

This tool compares Riemann and Lebesgue integration methods for computing the integral of a Gaussian PDF. The "Integral Value" shows the area under the curve (probability). The "Sample Mean" and "Sample Variance" are computed by treating the normalized PDF as a probability distribution and calculating the expected value and variance. For a standard normal distribution over [-∞,∞], these should approach 0 and 1 respectively.