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fundamental-theorem-of-calculus

Shows f(x) on the top panel with a moving upper limit x and blocky Riemann shading for the signed area ∫_a^x f(t)dt. The bottom panel graphs the accumulation function F(x) and draws a tangent whose slope dF/dx numerically matches the current f(x), illustrating FTC Part 1. A center annotation highlights FTC Part 2: ∫_a^b f(x)dx = F(b) − F(a).

canvasclick to interact
t=0s

practical uses

  • 01.Compute definite integrals via antiderivatives (evaluation theorem)
  • 02.Interpret integrals as accumulated change (area/accumulation models)
  • 03.Connect rates (derivatives) to totals (integrals) in physics and engineering

technical notes

Uses time-based sweep x=a→b with ease() for smooth motion. f(x) is sampled to scale axes; F(x) is computed each frame by a midpoint Riemann sum, and dF/dx is approximated with a centered finite difference. Rendering uses grid-snapped coordinates and Riemann bars for a retro blocky aesthetic on a black background with green highlights.