a

x

A

x + Δx

ΔA

A(x) = \int_{a}^{x} f(t) dt

A(x)

A(x+Δx)

f(x)

ξ

f(ξ)

A(x)

ΔA = A(x+Δx) - A(x)

Δx

ΔA

f(x) = 0.1 x² + 0.1 x + 1
P_A = Point(xAxis)
P_B = Point(xAxis)
I = Integral(f, x(P_A), x(P_B))
P_D: (x(P_B) + 5, 0)
a = Ray(P_B, P_D)
P_C = Point(a)
c = Integral(f, x(P_B), x(P_C))
h_1: c / Distance[P_B, P_C]
C: (x(P_C), h_1)
B: (x(P_B), h_1)
l = Segment(B, C)
F = Integral(f(x))
A(x) = F(x) - F(x(P_A))
I_1: (x(P_B), A(x(P_B)))
I_2: (x(P_C), A(x(P_C)))
d = Tangent(I_1, A)
K: (x(P_B), f(x(P_B)))
i = Segment(K, P_B)
G, G_1 = Intersect(f, l)
g = Segment(G, (x(G), 0))
P, p_b, p_c, c_1, b = Polygon(P_B, P_C, C, B)
H: (x(G), 0)
I_3: (x(I_2), y(I_1))
Q, i_2, i_1, i_3 = Polygon(I_1, I_3, I_2)
e = Segment((0, y(I_1)), I_1)
h = Segment((0, y(I_2)), I_2)
j = Segment((0, y(I_1)), (0, y(I_2)))
t = Function(A(x(P_B)) + f(x(P_B)) (x - x(P_B)), x(P_B) - 1, x(P_B) + 1)
t_1 = Tangent(x(P_B), A)
k = Slope(t_1)
T15: "f(x)=" + (f(x(P_B)))