Which of the following expressions equals the right‐endpoint Riemann sum with equal…

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

Problem

Which of the following expressions equals the right‐endpoint Riemann sum with

n

equal subintervals that approximates

\displaystyle \int_{2}^{5} \frac{1}{x}\,dx

? (a)

\displaystyle \sum_{k=0}^{n-1} \frac{1}{2+\dfrac{3k}{n}}\cdot\frac{3}{n}

(b)

\displaystyle \sum_{k=1}^{n} \frac{1}{2+\dfrac{3k}{n}}\cdot\frac{3}{n}

(c)

\displaystyle \sum_{k=1}^{n} \frac{1}{2+\dfrac{3(k-0.5)}{n}}\cdot\frac{3}{n}

(d)

\displaystyle \sum_{k=1}^{n} \frac{1}{2+\dfrac{3k}{n}}\cdot\frac{n}{3}