Let be a positive function that is decreasing on the closed interval
MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change
Problem
Let f be a positive function that is decreasing on the closed interval [0,5]. Which of the following statements is true when uniform partitions are used to approximate ∫05f(x)dx?
(a) Both the left and right Riemann sums underestimate the integral.
(b) The left Riemann sum overestimates the integral, and the right Riemann sum underestimates it.
(c) The left Riemann sum underestimates the integral, and the right Riemann sum overestimates it.
(d) Without information about the concavity of f, it is impossible to know whether the left or right Riemann sum over- or underestimates the integral.