🟦 Riemann Sum Lab — Area Under Any Curve
🟦 Riemann Sum Lab — Area Under Any Curve
Type any function, drag the number of rectangles, and watch the classic left/right/middle/trapezoid sums close in on the true integral. Live shaded plot, error against a high-precision reference, and a convergence table that proves why doubling n quarters the trapezoid error.
—estimate (signed area)
—reference value
—error
—relative error
Reference: adaptive-Simpson computed to ~10 digits. “Signed” means parts below the axis count negative — that's why x³−3x on −2→2 is 0.
How fast the error shrinks
× ÷ and implicit products go left-to-right:
1/2x means (1/2)·x. Allowed: + − * / ^, parentheses, sin cos tan exp ln log sqrt abs, constants pi and e.