黎曼和与积分
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这个范例演示了黎曼和与积分的概念。通过调整分段数,可以观察到黎曼和如何逼近积分值。核心数学概念包括积分、黎曼和及其在几何上的应用。使用了函数、序列、构造区间、求和等GeoGebra命令。适合高中数学教学和学习微积分。
GeoGebra 命令及参数
CreatePanel(240) → poly1, aSelectedElement(Function) → fPoint(f) → APoint(f) → BLeftSum(f, x(A), x(B), n) → LeftSum_1Integral(f, x(A), x(B)) → Integral_1UpperSum(f, x(A), x(B), n) → UpperSum_1LowerSum(f, x(A), x(B), n) → LowerSumSequence(x(A) + (i * dx), i, 0, n) → subintTake(subint, 2, n + 1) → rightTake(subint, 1, n) → leftSequence(Polygon[(Element[left, i], 0), (Element[right, i], 0), (Element[right, i], Element[rightheights, i]), (Element[left, i], Element[rightheights, i])], i, 1, n) → rightRectLine(C, yAxis) → bLine(D, b) → cPoint(c) → EOrthogonalLine(E, b) → dOrthogonalLine(C, c) → ePoint(c) → FOrthogonalLine(F, b) → gPoint(b) → GOrthogonalLine(G, c) → hPoint(c) → HOrthogonalLine(H, b) → iPoint(c) → IOrthogonalLine(I, b) → jPoint(c) → JOrthogonalLine(J, b) → kPoint(c) → KOrthogonalLine(K, b) → lPoint(c) → LOrthogonalLine(L, b) → mPoint(b) → MOrthogonalLine(M, c) → pIntersect(b, d) → NIntersect(c, e) → OIntersect(c, h) → PPoint(b) → QIntersect(b, i) → RIntersect(b, j) → SIntersect(b, k) → TPoint(b) → UIntersect(b, m) → VIntersect(c, p) → WPolygon(N, C, O, E) → poly2, n_1, c_1, o, e_1Polygon(Q, G, P, F) → poly3, q, g_1, p_1, f_1Polygon(R, S, I, H) → poly4, r, s, i_1, h_1Polygon(T, U, K, J) → poly5, t, u, k_1, j_1Polygon(V, M, W, L) → poly6, v, m_1, w, l_1
AI 绘图提示语参考
绘制一个函数f在区间[A, B]上的积分图形,展示左和、右和、下和、上和的概念。通过构造一系列矩形来近似积分值,并绘制这些矩形与函数曲线的关系。图形应包含函数曲线、区间端点、矩形区域以及积分近似值。
以上提示语为根据原始绘图命令整理而来,仅供参考。