Mathematics

Problem

Write

\displaystyle \int_{2}^{8} \sqrt{x}\,dx

\displaystyle \lim_{N\to\infty}\sum_{i=1}^{N}(\,\cdot\,)

using

N

equal subintervals and midpoints. Give the explicit formula for the midpoint

x_i^{*}

and the fully simplified summand in terms of

i

and

N