x

B'(x)

Randfunktion f(x)

Integralfunktion I_a(x)

I_a(x)

a =

a

x+h

(I_a(x+h)-I_a(x))/h

\downarrow \quad h \rightarrow 0

\downarrow \quad h \rightarrow 0

I_a(x+h)-I_a(x)

Sekante

(I_a(x+h)-I_a(x))/h

I_a(x+h)-I_a(x)

I_a(x+h)-I_a(x)

m=(I_a(x+h)-I_a(x))/h

(I_a(x+h)-I_a(x))/h

Rechteck

X = Point(xAxis)
x0: x(X)
b: x0
a = 0 (slider from -5 to 5)
f(x) = (((0.1 * x) * (x - 3)) * (x - 6))
k = 0.5 (slider from 0 to 1)
Intervall = Segment((0 | 0), (7 | 0))
gl1: x = x(X)
I = Integral(f, a, b)
Eingabefeld1 = Textfield(a)
I0 = Integral(f, 0, a)
g(x) = Integral[f] - I0
A: (a | 0)
H = Point(xAxis)
IXH = Integral(f, x(X), x(H))
Ih = Integral(f, a, x(H))
IH: (x(H) | Ih)
IX: (x(X) | I)
h: x(H) - x(X)
IM: IXH / h
p: y = IM
B = Intersect(f, p, x0, x(H))
B0: (x(B) | 0)
i = Segment(B0, B)
g2: x = x(H)
R1: X
R2: H
R3: (x(H) | y(B))
R4: (x(X) | y(B))
R, r1, r2, r3, r4 = Polygon(R1, R2, R3, R4)
s = Line(IX, IH)
m = Slope(s)
QXH: (x(H) | I)
dI = Segment(QXH, IH)
e = true
j = false
d = false
l = false
m1 = Segment(IX, QXH)
m2 = Segment(QXH, IH)
n = false
o: f(x(X))
Text6: "\frac{I_a(x+h)-I_a(x)}{h} =" + (LaTeX[m]) + ""
Text1: "\frac{I_a(x+h)-I_a(x)}{h} =" + (LaTeX[m]) + ""
Text8: "I_a'(x) = " + (LaTeX[o]) + ""
Text5: "f(x) = " + (LaTeX[o]) + ""
c = false