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