The function is continuous on

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

The function

f

is continuous on

0\le x\le 6

, and the accumulation function

g

is defined by

g(x)=\int_{0}^{x} f(t)\,dt.

Values of

g

are shown in the table.

x \qquad 0 \qquad 2 \qquad 4 \qquad 6

g(x) \; 0 \qquad 3 \qquad 9 \qquad 18

Which of the following is closest to the average value of

f

on the interval

[2,6]

? (a)

4.5

(b)

3.75

(c)

3

(d)

2.5