A continuous function satisfies

MATHEMATICS · Subjective · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

A continuous function

v

satisfies

\displaystyle\int_{0}^{6} v(t)\,dt=18

. What numerical value does the limit

\lim_{n\to\infty}\sum_{i=1}^{n} v\!\left(\frac{6i}{n}\right)\frac{6}{n}

approach?