Let be continuous

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

Problem

Let

f

be continuous, decreasing, and concave up on

[2,8]

. Using the same number

n

of equal-width subintervals, let

L,\,R,\,M,

and

T

denote the left-endpoint, right-endpoint, midpoint, and trapezoidal approximations, respectively, of

\displaystyle \int_{2}^{8} f(x)\,dx

. Which ordering from least to greatest must always hold? (a)

L < T < M < R

(b)

R < M < T < L

(c)

M < R < T < L

(d)

R < T < M < L