c

d

a

b

Int_{ab}

h

f(x)=f_0(x)+h

g(h)=\int_a^b(f_0(x)+h)\,dx

g(0)

Pos

Int_{cd}

Bewerge h 
mit den Pfeiltasten

t = -0.5
a: 1
b = 4
a_1: 0.5
a_2: 3
a_3: 4.2
a_4: 1.5
h = -0.7 (slider from -5 to 5, step 0.1)
f_0(x) = ((((t * (x - a_1)) * (x - a_4)) * (x - a_2)) * (x - a_3)) + 1
f(x) = f_0(x) + h
Int_{ab} = Integral(f, a, b)
C, D = Roots(f, a, b)
Int_{db} = Integral(f, x(D), b)
Int_{ac} = Integral(f, a, x(C))
Su: Int_{ac} + Int_{db}
A: (a, 0)
B: (b, 0)
Int0_{ab} = Integral(f_0, a, b)
i(x) = (Int0_{ab} * x)
w_h: y = h
In: (h, Int_{ab})
h_1 = Segment((h, 0), In)
H: (0, h)
c = Integral(f_0(x) - h + 1, a, b)
Int_{cd} = Integral(f, x(C), x(D))
g = Locus(In, h)
S: (0, Int0_{ab})
P: (h, Su)
Ortslinie4 = Locus(P, h)
N: (h, Int_{cd})
Ortslinie5 = Locus(N, h)
O = (0, 0)
H_r: (h, 0)
j = Segment(H_r, O)
k = Segment(O, H)
E = (1.551816365202419, -1.1715741602067256)
F = (1.9653633074935517, -1.1715741602067256)