Module 6 : Definition of Integral
Lecture 16 : Integral as a limit of Riemann sums [Section 16.2]
6.
Prove that for all and
 


Hence, find  by computing the Riemann sums for a suitable sequence of partitions and taking limits.

7.
 Let be a non-negative continuous function such that ,for some . Show that there exist
 

, such that

         

Hence, deuce that

         

Hence,

if is non-negative continuous and , then for all .

8.
Give an example of a nonzero integrable function such that for all , but
           .
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