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.

Load Example Function:

Enter Function f(x):

Interval Start (a):

Interval End (b):

Subintervals (n): 10

Integration Method:

Midpoint Trapezoid Simpson's

True Integral (Area)

Midpoint Approximation

Absolute Error

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

n	Midpoint Error	Trapezoid Error	Simpson Error