The continuous function increases on and decreases on
MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change
Problem
The continuous function g increases on [0,2] and decreases on (2,5]. A left-endpoint Riemann sum with equally spaced subintervals is used to approximate ∫05g(x)dx. Which statement about the sign of the approximation error is necessarily true?
(a) The approximation is necessarily an overestimate.
(b) The approximation is necessarily an underestimate.
(c) The information provided is insufficient to determine the sign of the error.
(d) The approximation equals the exact integral only if g is symmetric about x=2.