Let be a continuous function that is strictly increasing on the closed interval

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Let

f

be a continuous function that is strictly increasing on the closed interval

[a,b]

. Which of the following numerical approximation methods must produce an underestimate of

\displaystyle \int_a^b f(x)\,dx

for any partition of

[a,b]

? (a)

\text{A trapezoidal sum}

(b)

\text{A right Riemann sum}

(c)

\text{A left Riemann sum}

(d)

\text{A midpoint Riemann sum}