CK12 Calculus - Single Variable

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.