In this worksheet you will investigate the area under the function [math]f(x) = \sqrt{x-1}[/math] from x=2 to x=5.[br][br]The actual area of the region can be approximated by rectangles of various heights, each having the same base.[br]GeoGebra will calculate the sum of the areas of each rectangle for you.[br][br]Use the first slider to change the number of approximating rectangles.[br][br]When each rectangle intersects the graph of f(x) at its top left endpoints, the sum of the areas is called the [b]Left Riemann Sum[/b]. When each rectangle intersects the graph of f(x) at its right enpoints, the sum is called the [b]Right Riemann Sum[/b]. When each rectangle intersect f(x) at the midpoint of its top left and right endpoints, the sum is called the [b]Midpoint Riemann Sum[/b].

Test Your Understanding:[br][br]1.) Set the first slider to n=6. What is the length of the base of each rectangle? If n = 7, how would you calculate the length of each base? For an arbitrary number "n", what is the base?[br][br]2.) Set "n=6" and choose "Left Endpoint". How would you calculate the heights of each six rectangles? How would your calculation change if you chose "Right Endpoint" instead? What would change if you chose "Midpoint"?