linke Intervallgrenze: 

rechte Intervallgrenze: 

Mittelwert einer stetigen Funktion

Mittelwert anzeigen

Fläche oberhalb und unterhalb anzeigen

(anklicken!)

(haj v 1.1)

f(x) = 1 / 2500 * x^(4) - 1 / 125 * x^(3) - 14 / 625 * x^(2) + 192 / 625 * x + 6
a = 1 (slider from -3 to 22, step 0.25)
b = 14 (slider from -3 to 22, step 0.25)
I_{ab} = Integral(f, a, b)
iw = Integral(f, a, b)
mw: Integral[f, a, b] / (b - a)
m(x) = mw
I_{diff} = IntegralBetween(f, m, a, b)
d: b - a
T4: "m =  \frac{ 1 }{b-a }  \;  \int_{a }^{b }f(x)dx \;=\;\; \frac{ 1}{" + d + "}\;*\; \int_{" + a + " }^{\;" + b + " }f(x)dx\;=\;\;\frac{" + I_{ab} + "}{" + d + "}\;=\;\;" + mw
c = false
e = false