Which expression gives the average value of a continuous function on the closed…

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

Problem

Which expression gives the average value of a continuous function

f

on the closed interval

[a,b]

(with

a<b

)? (a)

f\!\left(\dfrac{a+b}{2}\right)

(b)

\dfrac{1}{b-a}\displaystyle\int_{a}^{b} f(x)\,dx

(c)

\dfrac{1}{b}\displaystyle\int_{a}^{b} f(x)\,dx

(d)

\dfrac{f(a)+f(b)}{2}