黎曼和
Author: 藍邦偉  老師

$%v等分$

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$ 黎曼和 $

$ 上黎曼和 $

$ 下黎曼和 $

$ 右黎曼和 $

$ 左黎曼和 $

$ 黎曼和 $

$梯形法$
$ (辛普森法) $

$ 實際面積 $

F = (6.261774230009248, -0.026464587573709675)
B = DynamicCoordinates(F, floor(x(F)), 0)
E = (-4.333763867671323, 0.042189007011693716)
A = DynamicCoordinates(E, floor(x(E)), 0)
n = 21 (slider from 1 to 50, step 1)
k = 0 (slider from 0 to 2, step 1)
s = 0.28 (slider from 0 to 1, step 0.01)
a = Min(x(A), x(B))
d: (x(B) - x(A)) / n
f(x) = sin(x) + 2 * sin(x / 2) + 4
b = Max(x(A), x(B))
Area_1 = Integral(f, a, b)
c_1 = 0
u = Vector((x(Corner[1]), 0), (x(Corner[3]), 0))
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))
T2 = false
T1 = false
T7 = false
T6 = false
C: (x(A), f(x(A)))
D: (x(B), f(x(B)))
i = Segment(C, A)
j = Segment(D, B)
list1 = Sequence(x(A) + If[k ≟ 0, (t + s * 0 + random()) * d, If[k ≟ 1, t * d, (t + 1) * d]], t, 0, n - 1)
list2 = Sequence(Polygon[(x(A) + (t - 1) * d, 0), (x(A) + t * d, 0), (x(A) + t * d, f(Element[list1, t])), (x(A) + (t - 1) * d, f(Element[list1, t]))], t, 1, n)
list3 = Sequence(Segment[(Element[list1, i], 0), (Element[list1, i], f(Element[list1, i]))], i, 1, n)
L_n = LowerSum(f, a, b, n)
U_n = UpperSum(f, a, b, n)
T_n = TrapezoidalSum(f, a, b, n)
T5 = false
lista = Sequence(Polygon[(a + (i - 1) * d, 0), (a + i * d, 0), (a + i * d, f(a + i * d)), (a + (i - 1) * d, f(a + i * d))], i, 1, n)
listb = Sequence(Polygon[(a + (i - 1) * d, 0), (a + i * d, 0), (a + i * d, f(a + (i - 1) * d)), (a + (i - 1) * d, f(a + (i - 1) * d))], i, 1, n)
T4 = false
T3 = false
Q_4: 0.25 * Corner[4] + 0.75 * Corner[1]
Q_3: (x(Corner[2]), y(Q_4))
poly1, c, e, q_3, q_4 = Polygon(Corner[1], Corner[2], Q_3, Q_4)
ia: i * a
t_b: "$ " + (LaTeX[If[a < b, "b", "a"]]) + " $"
t_{area}: "$R= \int_{" + (LaTeX[a]) + "}^{" + (LaTeX[b]) + "}{f(x)dx }=" + (LaTeX[Area_1]) + " $"
t_a: "$ " + (LaTeX[If[a < b, "a", "b"]]) + " $"