Mathematics

Mathematics

Problem

For a continuous function that is strictly increasing on [a,b][a,b], a right–endpoint Riemann sum with nn equal-width subintervals is used to approximate ∫abf(x) dx\displaystyle \int_a^b f(x)\,dx. Which of the following best describes the sign of the approximation error? a) The approximation is greater than the exact value of the integral. b) The approximation is greater than the exact value only if ff is concave down; otherwise it is less. c) The approximation is less than the exact value of the integral. d) The approximation may be greater or less than the exact integral depending on the number of subintervals nn.

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