Consider on the interval

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

Problem

Consider f(x)=exf(x)=e^{x} on the interval [0,1][0,1]. A midpoint Riemann sum with two equal-width subintervals is used to approximate ∫01ex dx\displaystyle \int_{0}^{1} e^{x}\,dx. Which statement about the approximation is correct? (a) It overestimates the integral because ff is increasing on [0,1][0,1]. (b) It overestimates the integral because ff is concave up on [0,1][0,1]. (c) It underestimates the integral because ff is concave up on [0,1][0,1]. (d) It gives the exact value of the integral because the midpoint rule is exact for exe^{x} on [0,1][0,1].

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