Numerical Integration Lab

Approximate the area under a curve by summing the areas of simpler shapes. Compare the accuracy of the Midpoint, Trapezoidal, and Simpson's rules.

True Integral (Area)
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Midpoint Approximation
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Absolute Error
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Error Analysis

Investigate how the approximation error changes as the number of rectangles (n) increases. For the Midpoint and Trapezoid rules, the error is expected to decrease proportionally to 1/n². Simpson's rule error decreases much faster, proportionally to 1/n⁴.

Raw Data

nMidpoint ErrorTrapezoid ErrorSimpson Error