MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change
Problem
Let f be a positive, decreasing function on [1,5]. A sum is formed by multiplying the width of each subinterval in a partition 1=x0<x1<x2<x3=5 by the value of f at the left endpoint of that subinterval and then adding the results. Which statement best describes this sum relative to ∫15f(x)dx?
(a) It is an underestimate because f is decreasing on [1,5].
(b) It could be an overestimate or an underestimate depending on the concavity of f on [1,5].
(c) It is an overestimate because f is decreasing on [1,5].
(d) Whether it is an overestimate or an underestimate cannot be determined without a uniform partition.