integrals #

Shows a definite integral as a Riemann-sum approximation with rectangles whose count increases toward a limit, highlighting dx as the rectangle width. The lower panel shows the indefinite integral as an antiderivative family F(x)+C, and animates the Fundamental Theorem of Calculus by comparing F(b) and F(a) so their difference matches the accumulated area.

canvasclick to interact

⏮◀◀▶▶STEP0.25x1xZOOM

t=0s

practical uses #

01.Compute areas/accumulated change from sampled rates (physics: distance from velocity)
02.Numerical integration via Riemann sums/rectangles (engineering approximations)
03.Solve differential relationships by finding antiderivatives (control systems, growth models)

technical notes #

Pure Canvas2D. Responsive scaling via scale=min(w,h)/240 and grid snapping for a blocky look. Time-based animation cycles: N ramps 4→32 for Riemann rectangles; a sweeping highlight shows dx. Antiderivative family uses multiple curves with animated constant C; FTC panel animates b sliding and displays F(b)-F(a).

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