With our definitionand initialexample,we now look to formalizethe definitionand developsomeusefulrules
for computationalpurposes,and beginto see someapplications.
Notationand Introductionto IndefiniteIntegrals
The processof findingantiderivativesis calledantidifferentiation, morecommonlyreferredto asintegra-
tion. We havea particularsign and set of symbolswe use to indicateintegration:
We refer to the left side of the equationas “the indefiniteintegralof with respectto " The function
is calledthe integrand and the constant is calledthe constantof integration. Finallythe
symbol indicatesthat we are to integratewith respectto
Usingthis notation,we wouldsummarizethe last exampleas follows:
UsingDerivativesto DeriveBasicRulesof Integration
As with differentiation,thereare severalusefulrulesthat we can deriveto aid our computationsas we solve
problems.The first of theseis a rule for integratingpowerfunctions, and is stated
as follows:
We can easilyprovethis rule. Let. We differentiatewith respectto
and we have: