Module 6 : Definition of Integral
Lecture 16 : Integral as a limit of Riemann sums [Section 16.2]
2.
 Assuming that is integrable on a suitable interval, express
 

          
as an integral for a suitable function .

3.

For the function

 

          
obtain a Riemann sum for a suitable sequence of partitions and compute
          .
4.

Let be a nonzero integrable function such that

 

          .
Show that
          
even though for any .
5.
 Let be an integrable function such that
 

          for all

where Show that

           .

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