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multiple-integrals #

Shows a non-rectangular 2D integration region R partitioned into grid cells (ΔA), highlights a moving differential element dA, and builds the signed volume under z=f(x,y) using Riemann-sum boxes. In the latter part of the animation, a scanning slice illustrates Fubini’s theorem by accumulating the same total via different iterated-integration orders (dx then dy vs dy then dx).

canvasclick to interact

⏮◀◀▶▶STEP0.25x1xZOOM

t=0s

practical uses #

• 01.Compute volumes and signed volumes under surfaces z=f(x,y) over irregular regions
• 02.Mass/charge totals from density functions over an area or volume
• 03.Change of order / iterated integrals (Fubini) for simpler evaluation in applied problems

technical notes #

Pure Canvas2D rendering with a snapped grid for a retro blocky aesthetic. Uses time-based phases (4.2s loop): partition refinement + Riemann-sum assembly, then Fubini scanline highlighting. Volume is drawn with a lightweight pseudo-3D projection and per-cell extrusion; positive/negative heights use different green intensities to emphasize signed volume.

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