积极 AI Logo 积极 AI

矩形区域上的二重积分

矩形区域上的二重积分
几何画板及绘图内容加载中，请稍等……
2020-05-16 02:15
函数微积分积分
①本范例演示了如何在矩形区域内计算二重积分的几何意义；②涉及的核心数学概念包括积分、函数图象、微分几何；③作图要点——从下方『构造摘要』提炼用到了Polygon（多边形）、Prism（棱柱）等GeoGebra命令/对象；④适合高中及以上学生学习和理解积分的应用。

GeoGebra 命令及参数

  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