Compare Left, Right, Midpoint, Trapezoidal & Simpson's Rule
Left/Right Riemann sums use endpoint heights (O(1/n) error). Midpoint uses center of each sub-interval (O(1/n²)). Trapezoidal uses trapezoids instead of rectangles (O(1/n²)). Simpson's rule fits parabolas through every 3 points, giving O(1/n⁴) accuracy — the best for smooth functions. Watch the error percentages shrink as you increase n!