a = 1 (slider from -5 to 5, step 0.1)
b = 3 (slider from -5 to 5, step 0.1)
c = 1 (slider from -5 to 5, step 0.1)
f(x) = a * x * (x - b)^(2.0) + c
N_1, N_2, N_3 = Intersect(f, xAxis)
f'(x) = f'(x)
f''(x) = f''(x)
W_0 = Intersect(f'', xAxis)
d = OrthogonalLine(W_0, xAxis)
W = Intersect(f, d)
w_T = Tangent(W, f(x))
B = Intersect(w_T, yAxis)
A = Intersect(w_T, xAxis)
Vieleck1, s, a_1, b_1 = Polygon(A, B, (0.0, 0.0))
h: 32.0 * a^(2.0) * b^(4.0) / 243.0
k = Circle(W, 4.0)
P = Point(k)
i = Line(P, W)
S_1, D, S_2 = Intersect(f, i)
C = Intersect(i, yAxis)
g(x) = (y(W) - y(P)) / (x(W) - x(P)) * x + y(C)
j = Integral(f(x) - g(x), x(S_1), x(W))
l = Integral(g(x) - f(x), x(W), x(S_2))
m = Integral(g(x), x(S_1), x(W))
n = Integral(g(x), x(W), x(S_2))
o = Integral(f(x), x(S_1), x(W))
p = Integral(f(x), x(W), x(S_2))
Text1: "A_1 = " + (Integral[f(x) - g(x), x(S_1), x(W)])
Text2: "A_2 = " + (Integral[g(x) - f(x), x(W), x(S_2)])