Wat is de gemiddelde waarde
( = middelwaarde )
van de functie   f (x) = 4 − x2
over het interval   [ − 2, 2 ] ?
A.   \(\boldsymbol{\frac{16}{3}}\)
B.   \(\boldsymbol{2}\)
C.   \(\boldsymbol{\frac{8}{3}}\)
D.   \(\boldsymbol{4}\)
E.   \(\boldsymbol{\frac{4}{3}}\)
F.   \(\boldsymbol{\frac{32}{3}}\)
G.   \(\boldsymbol{\frac{128}{3}}\)
A   B   C   D   E   F   G

[ 6-5236 - op net sinds 11.2.13-(E)-16.10.2026 ]

Translation in   E N G L I S H

What is the average value
of the function   f (x) = 4 − x2
over the interval [ − 2, 2 ] ? 		A.  \(\boldsymbol{\frac{16}{3}}\)
B.   \(\boldsymbol{2}\)
C.   \(\boldsymbol{\frac{8}{3}}\)
D.   \(\boldsymbol{4}\)
E.   \(\boldsymbol{\frac{4}{3}}\)
F.  \(\boldsymbol{\frac{32}{3}}\)
G.  \(\boldsymbol{\frac{128}{3}}\)

Oplossing - Solution

\(\frac{1}{2-(-2)}\int_{-2}^{2}(4-x^2)\;dx=\frac14\left[4x-\frac{x^3}{3}\right]_{-2}^2=\frac14\left[\left(4.2-\frac{2^3}{3}\right)-\left(4(-2)-\frac{(-2)^3}{3}\right)\right]\\=\frac14\left[8-\frac83+8-\frac83\right]=\frac14\left[16-\frac{16}{3}\right]=4-\frac43=\frac{12-4}{3}=\frac83\)