Mathematics

Problem

Consider the definite integral

\displaystyle\int_{1}^{3} x^{2}\,dx

. Using four equal subintervals, a student forms both the left-hand and right-hand Riemann sums,

L_{4}

and

R_{4}

. Which of the following intervals is guaranteed to contain the exact value of the integral? a)

(6.75,\,8.75)

(8.75,\,10.75)

(6.75,\,10.75)

(7.75,\,9.25)