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Double Integrals over Rectangles

Double Integrals over Rectangles
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2020-05-16 02:15
FunctionCalculusIntegral
This example demonstrates the calculation of double integrals over rectangular regions, involving integral concepts, function graphs, and differential geometry. It uses GeoGebra commands like Polygon and Prism for construction, suitable for high school and above learning integral applications.

GeoGebra Commands & Parameters

  1. Polygon((0, 1, 0), (1, 1, 0), (1, 2, 0), (0, 2, 0)) → q2, f, g, h, i
  2. Prism(q2, (0, 1, 3)) → c, A, edge2, edge3, edge4, edge5, edge6, edge7, edge8, B, C, face1, face2, face3, face4, face5, edge1
  3. Polygon((1, 0, 0), (2, 0, 0), (2, 1, 0), (1, 1, 0)) → q1, j, k, l, m
  4. Prism(q1, (1, 0, 1.5)) → b, D, edge10, edge11, edge12, edge13, edgeDE, edgeEF, edge14, E, F, face6, face8, face9, face7, face10, edge9
  5. Polygon((1, 1, 0), (2, 1, 0), (2, 2, 0), (1, 2, 0)) → q3, n, p, q, r
  6. Prism(q3, (1, 1, 0)) → d, G, edge16, edge17, edge18, edge19, edge20, edge21, edge22, H, I, face11, face12, face13, face14, face15, edge15
  7. Polygon((0, 0, 0), (1, 0, 0), (1, 1, 0), (0, 1, 0)) → q4, t, e, f_1, g_1
  8. Prism(q4, (0, 0, 4.5)) → o, J, edge24, edge25, edge26, edge27, edgeJK, edgeKL, edge28, K, L, face16, face18, face19, face17, face20, edge23