🟦 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.

f(x)

from a

to b

rectangles n = 8

Left Right Midpoint Trapezoids

—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.