Example 12.   Let    over  .  Use the Lower Riemann Sum to approximate the value of the integral.

Solution 12.

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

Animation 3.  ( Lower Riemann Sum  Lower Riemann Sum ).  Internet hyperlink.

(c) John H. Mathews 2004