Simpson-Regel

\frac{1}{3} (y_0 + 4y_1 + 2y_2 + 4y_3 + y_4)

C: (2, 0)
A: (1, 0)
n = OrthogonalLine(A, xAxis)
f(x) = sqrt(16 - (x - 4)^(2))
J = Intersect(f, n, (1, 2.6457513110645907))
h = OrthogonalLine(C, xAxis)
B: (3, 0)
i = OrthogonalLine(B, xAxis)
E = Intersect(f, h, (2, 3.4641016151377544))
F = Intersect(f, i, (3, 3.872983346207417))
a = Integral(f, 0, 2)
b = Integral(f, 2, 4)
y_3 = Segment(F, B)
c: a + b
H = Point(xAxis)
k = OrthogonalLine(H, xAxis)
I = Intersect(f, k, (4, 4))
y_4 = Segment(I, H)
y_1 = Segment(J, A)
q = Segment(C, E)
y_2: q
par(x) = ((-0.9137) * x^(2)) + (3.55940972 * x)
delta_1 = IntegralBetween(f, par, 0, 2)
pp(x) = ((-0.1409) * x^(2)) + (1.1135 * x) + 1.8
delta_2 = IntegralBetween(f, pp, 2, 4)
O: (0, 0)
y_0: 0
simpson: (1 / 3 * (y_0 + (4 * y_1) + (2 * y_2) + (4 * y_3) + y_4))
Text7: "=" + simpson + ""
VK: (4 * π)
Text1: "Viertelkreis=" + VK + ""