FromTheorem4.1 we havethat is an antiderivativeof Hence, and in particular,
Hence,by substitutionwe have
Notethat Hencewe have
and by our definitionof we have
This theoremallowsus to find for positivefunctionsa rectanglethat has base and height such
that the area of the rectangleis the sameas the area givenby In otherwords, is the
averagefunctionvalueover
ReviewQuestions
In problems#1–8,use antiderivativesto computethe definiteintegral.