Mathematics

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}

\text{A right Riemann sum}

\text{A left Riemann sum}

\text{A midpoint Riemann sum}