Mathematics

Problem

For a continuous function

f

that is strictly increasing on

[2,7]

L_{5}

and

R_{5}

denote the left- and right-hand Riemann sums with five equal subintervals for

\displaystyle\int_{2}^{7} f(x)\,dx

. Which of the following describes the relationship among

L_{5}

R_{5}

, and the exact value of the integral? a)

L_{5} < R_{5} < \displaystyle\int_{2}^{7} f(x)\,dx

\displaystyle\int_{2}^{7} f(x)\,dx < L_{5} < R_{5}

L_{5} < \displaystyle\int_{2}^{7} f(x)\,dx < R_{5}

R_{5} < \displaystyle\int_{2}^{7} f(x)\,dx < L_{5}