Partition & Function Viewport
Hover/Drag canvas to inspect sub-intervals
⚙️ Simulation Parameters
📈 Absolute Error $|S_n - I|$ vs. $n$
O(1/n) Convergence📐 Computed Proof & Limits
VALIDATED CONVERGENCE
PARTITION (n)
8
SLICE Δx
0.5000
RIEMANN S_n
3.9375
ABS ERROR
0.0625
At n = 8 partitions, the sub-interval width is Δx = 0.5000. The finite approximation sum $S_n = 3.9375$ differs from the exact definite integral $I = 4.0000$ by 0.0625. As $n \to \infty$, $\Delta x \to 0$, driving residual error to zero.