Example 13.   Let    over  .  Use the Upper Riemann Sum to approximate the value of the integral.

Solution 13.

Remark.  This will be slow because many minimums need to be approximated.
You can skip the calculation and look at the recorded results. Change 4 to 20 to get all of the table.

        

m sample points	UpperRiemann[a,b,m]
1
2
4
6
8
10
12
14
16
20
24
28
32
40
50
60
70
80
100
120

  

Animation 4.  ( Upper Riemann Sum  Upper Riemann Sum ).  Internet hyperlink.

(c) John H. Mathews 2004