Chapter 5.3, Problem 3E

Evaluating a Limit In Exercises 3 and 4, use Example 1 as a model to evaluate the limit

$\underset{n\to \infty }{\lim }{\displaystyle \underset{i=1}{\overset{n}{\sum }}f\left(c_i\right)\Delta x_i}$

Over the region bounded by the graphs of the equations.

$f\left(x\right)=\sqrt{x},y=0,x=0,x=3\left(\text{Hint}:\text{Let}{c}_i=\frac{3i^2}{n^2}.\right)$