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Integration Derivatives

The area function A(x) sweeps out the region under f from a to x. Shrink the strip width Δx to zero and the strip's area, divided by Δx, settles on the curve's own height — f(x). That's the Fundamental Theorem of Calculus, watched live.

Strip, magnified

Area (pink) ÷ Δx = height (green line) — watch it meet f(x)

Controls

A(x) fill
Rectangle
▸ Shrink Δx → 0 (auto)
Drag the orange point on the curve to move x. Drag its right edge to resize the strip directly on the canvas.

Live numbers

Area under curve, A(x)0.000
Strip area, ΔA = A(x+Δx) − A(x)0.000
Strip width, Δx0.000
Height = ΔA ÷ Δx0.000
Actual f(x)0.000
|ΔA/Δx − f(x)| = 0.000