A Riemann sum is written as for the integral of a continuous function over

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

Problem

A Riemann sum is written as lim⁡n→∞∑i=1nf ⁣(a+(i−1)Δx) Δx\displaystyle \lim_{n\to\infty}\sum_{i=1}^{n}f\!\bigl(a+(i-1)\Delta x\bigr)\,\Delta x for the integral of a continuous function ff over [a,b][a,b]. Which statement correctly describes the sample points used in each subinterval? (a) They are the averages of the left and right endpoints (trapezoidal rule). (b) They are the right endpoints of each subinterval. (c) They are the left endpoints of each subinterval. (d) They are the midpoints of each subinterval.

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