a

A

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

b

A(b)

F(a)

F(b)

A(a)

f(x) = 0.1 (x - 0.13211206559108923)² + 0.1 (x - 0.13211206559108923) + 1.4756034361279224
P_B = Point(xAxis)
P_A = Point(xAxis)
F_1 = Integral(f(x))
A(x) = F_1(x) - F_1(x(P_A))
P_D: (x(P_B) + 5, 0)
a = Ray(P_B, P_D)
I = Integral(f, x(P_A), x(P_B))
I_1: (x(P_B), A(x(P_B)))
d = Tangent(I_1, A)
k = Slope(d)
K: (x(P_B), f(x(P_B)))
b = Segment(I_1, P_B)
c = 5 (slider from -10 to 10, step 0.2)
F(x) = F_1(x) + c - F_1(x(P_A))
B: (x(P_A), F(x(P_A)))
C: (x(P_B), F(x(P_B)))
D: (0, F(x(P_B)))
E: (0, F(x(P_A)))
g = Segment(E, B)
h = Segment(D, C)
i = Segment(D, E)
e = Segment(B, P_A)
j = Segment(C, P_B)
T1: "F(b) - F(a) = " + (y(I_1))
T5: "A(b) - A(a) = " + i