The following sum
\sqrt{6 + \frac{2}{n}} \cdot \left( \frac{2}{n}\right) +
\sqrt{6 + \frac{4}{n}} \cdot \left( \frac{2}{n}\right) +
\ldots + \sqrt{6 + \frac{2 n}{n}} \cdot \left( \frac{2}{n}\right)
is a right Riemann sum for the definite integral
\int_{3}^b f(x)\, dx

whereb =

andf(x) =

where

and

It is also a Riemann sum for the definite integral

where

and

The limit of these Riemann sums as

You can earn partial credit on this problem.