For a continuous function defined on

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

Problem

For a continuous function

f

defined on

[a,b]

, which of the following expressions gives the average value of

f

over the interval? (a)

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

(b)

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

(c)

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

(d)

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