Problem:
Graphically illustrate the definition of Riemann Sums for the function, y = f(x) with domain [a, b], whose graph is The blue line in the graph is part of the x-axis.

Note. The definition of Riemann Sums will be given in the development that follows.

Visualization:

If you want to view some additional graphs illustrating Riemann Sums with different values of n and different choices of xi's, then make your choices from the following two groups of options:

 Choose number of subdivisions: n = 10 n = 20 n = 40 Type: xi is right-hand endpoint of subinterval xi is left-hand endpoint of subinterval xi is midpoint of subinterval |f(xi)| is the maximum of |f| on the subinterval (circumscribed rectangles) |f(xi)| is the minimum of |f| on the subinterval (inscribed rectangles)

Note that the Riemann sum when each xi is the right-hand endpoint of the subinterval [ai-1, ai] is when each xi is the left-hand endpoint of the subinterval [ai-1, ai] is and when each xi is the left-hand midpoint of the subinterval [ai-1, ai] is .