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Motivation
Adding up a function in small pieces
Other questions
Content
The area under a graph
Estimates of area
Definition of the integral
Area and the antiderivative
Antiderivatives and indefinite integrals
Calculating areas with antiderivatives
Velocity–time graphs
Areas above and below the axis
Properties of the definite integral
Area between two curves
Links forward
Integration and three dimensions
Arc length
Difficulties with antiderivatives
History and applications
Appendix
A comparison of area estimates, and Simpson's rule
Exactness of area estimates
Functions integrable and not
Answers to exercises
References
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Integration
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Motivation and knowledge
Calculus: Module 15
Integration
Knowledge
Motivation - Adding up a function in small pieces
Motivation - Other questions
Content - The area under a graph
Content - Estimates of area
Content - Definition of the integral
Content - Area and the antiderivative
Content - Antiderivatives and indefinite integrals
Content - Calculating areas with antiderivatives
Content - Velocity–time graphs
Content - Areas above and below the axis
Content - Properties of the definite integral
Content - Area between two curves
Links forward - Integration and three dimensions
Links forward - Arc length
Links forward - Difficulties with antiderivatives
History and applications
Appendix - A comparison of area estimates, and Simpson's rule
Appendix - Exactness of area estimates
Appendix - Functions integrable and not
Answers to exercises
References
