Can someone help me set up the Riemann sum for y=sqrt(x)?
I have tried several times to set this up, but I cannot seem to simplify the summation. Any advice would be great!
I will assume you want the integral from $\displaystyle 0$ to $\displaystyle 1$ since then you can find the integral over a general interval by making appropriate transformations to the variables etc, and note nobody said the partitions had to be into equal intervals)
Take the partition:
$\displaystyle \left\{[0,(1/n)^2), [(1/n)^2,(2/n)^2), ... , [(\frac{n-1}{n})^2,1) \right\}$
Using this partition the left and right Riemann sums will reduce to something you should be able to handle.
CB