Chapter 8: Integration
The definition of integration is quite complicated and we devote some
time to studying that. We identify a class of "integrable" functions
wihich is analogous to the "differentiable" functions of Chapter 4
, and show that all continuous functions are integrable.
Evaluating the integral based on the definition alone is very hard, so
we prove the Fundamental theorem of calculus
; the theoretical tool which is the basis of all the integration techniques in calculus.
We then develop a more general theory of integration called
. This enables us to unify integration and summation; something which is useful in applications in mechanics and statistics, to name two.