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Multiple integrals: Fubini equality

What you are seeing: a heatmap of f(x,y)=sin⁡xcos⁡yf(x, y) = \sin x \cos y on [0,A]×[0,B][0, A] \times [0, B]. Two integration orders (dx dydx\,dy vs dy dxdy\,dx) give numerically identical values, illustrating Fubini's theorem.

Figure 1. Iterated integrals over a rectangle.
A (x-bound)3.14
B (y-bound)2.50

WHAT TO TRY

  • Vary each control and watch the rail readouts respond.
  • Compare the diagnostic plot against the live scene.