Let be a positive

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

Problem

Let

g

be a positive, decreasing function on

[0,4]

. The interval is subdivided into

8

equal subintervals, and the right endpoints are used to approximate

\displaystyle \int_0^4 g(x)\,dx

. Which of the following best describes the resulting approximation? (a) It is an overestimate because each rectangle lies above the graph of

g

. (b) It could be either an overestimate or an underestimate depending on the concavity of

g

. (c) It is an underestimate because each rectangle lies below the graph of

g

. (d) It equals the exact integral value because the number of subintervals is even.