AP Calculus ABmediummcq1 pt

Which of the following is the midpoint Riemann sum for 121xdx\int_1^2 \frac{1}{x}\,dx with two subintervals of equal width?

A.56\frac{5}{6}
B.712\frac{7}{12}
C.1724\frac{17}{24}
D.2435\frac{24}{35}

Explanation

Core Concept

The midpoints are x=1.25x=1.25 and x=1.75x=1.75, so the sum is 0.5(45+47)=24350.5\left(\frac{4}{5}+\frac{4}{7}\right)=\frac{24}{35}.

Correct Answer

D2435\frac{24}{35}

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