Áreas

Primitivas

h = f - g

Área \; bajo \; f(x) \; = \; 2(\pi-1)

Área \; sobre \; g(x) \; = \; 2(\pi+1)

$ F(2)-F(-2)=2(\pi-1) $

$ G(2)-G(-2)=-2(\pi+1)$

$ H(2)-H(-2)=4\pi $

Área \; bajo \; h(x) \; = \; 4\pi

Transforma

Partir

cero = 0
d = 0 (slider from 0 to 0.5, step 0.1)
achata: (1 + sqrt(17 + cero)) / 2
α: acos(sqrt((17 - sqrt(17) - cero) / 34))
polígono1: {Polygon[{(-10, 10), (-10, -10), (20, -10), (20, 10)}]}
p = Circle((0, 0), 2)
f0(x) = abs(x) / 2 + sqrt(4 - x^(2)) - 1
g0(x) = abs(x) / 2 - sqrt(4 - x^(2)) - 1
f(x) = f0(x) + d
g(x) = g0(x) - d
F = Integral(f0)
c_1 = 0
G = Integral(g0)
c_2 = 0
H0(x) = F(x) - G(x)
partío = false
a = false
corazón = false
b = false
t = 0 (slider from -0.5 to 6, step 0.01)
t1 = Max(Min[2 + ((achata - 2) * t), achata], 2)
t2 = Min(Max[0, t - 1.5], 1)
t3 = Min(Max[0, t - 3], 1)
t4 = Min(Max[0, t - 4.5], 1)
elip: x^(2) / t1^(2) + (y + t2)^(2) / (4 / t1)^(2) = 1
c(x) = d + (0 * x)
corInf(x, y) = y ≥ g(x) ∧ x ≥ -2 ∧ x ≤ 2 ∧ y ≤ g(2)
corSup(x, y) = y ≤ f(x) ∧ x ≥ -2 ∧ x ≤ 2 ∧ y ≥ f(2)
G2: (2 * (G(0) - G(-2)))
H = Simplify(H0)
h0(x) = f(x) - g(x)
h = Simplify(h0)
d3 = IntegralBetween(h, c, -2, 2)
bb1 = IntegralBetween(f, c, -2, 2)
bb2 = IntegralBetween(g, c, -2, 2)
elipseDinámica' = Rotate(elip, (α * t3), (0, -1))
B = Point(elipse1)
C = Point(elipse1)
D = Point(elipse1)
I = Point(elipse1)
J = Point(elipse1)
B' = Mirror(B, l)
C' = Mirror(C, l)
D' = Mirror(D, l)
I' = Mirror(I, l)
J' = Mirror(J, l)
P1: B + (t4 * (B' - B))
P2: C + (t4 * (C' - C))
P3: D + (t4 * (D' - D))
P4: I + (t4 * (I' - I))
P5: J + (t4 * (J' - J))
k = Conic(P1, P2, P3, P4, P5)
q = Arc(k, (0, 1), (0, -3))
r = Arc(elipse1, (0, -3), (0, 1))
texto1 = LaTeX(f, true, true)
texto2 = LaTeX(g, true, true)
texto3 = LaTeX(F, true, true)
texto4 = LaTeX(G, true, true)
texto9 = LaTeX(H, true, true)
texto11 = LaTeX(h, true, true)