Integration
Section overview:
The PowerPoint below provides an overview of material in this topic, including explanations and examples - for the full experience, open in a new tab then download it. All exercise references are to the new specification Pearson textbook - you can access the digital version for free or buy your own for extra practice.
Written summary notes are also given below for quick revision of key points, plus a selection of exam-style questions (with solutions) to test your understanding.
P1-Chp13-Integration.pptx
Notes:
Section 1 Notes - Indefinite integration and finding constants
Section 2 Notes - Definite integration and areas
Section 3 Notes - Negative/fractional indices and applications
Section 4 Notes - Integration as the limit of a sum
Summary questions:
The Calculus Project:
The following resources are designed to independently develop your geometric appreciation of A-level calculus alongside the classroom teaching. This is the most important part of A-level Maths, so it is vital you have a good understanding of it all!
Phase 2:
Explore the independent GeoGebra resources through the link to the right (as with most sites, it is best to use a browser other than Internet Explorer to access this).
Use the document below to help direct your investigations:
Extra resources:
Use the videos below to support your understanding of the topic. The ones on the left are specific to the course, building up to demos of exam-style questions; the ones on the right are for your own amusement, although the alternative outlook may provide you with a deeper overall understanding and appreciation of the topic.
In particular, 'The Essence of Calculus' video series is dotted throughout the relevant topic pages in A-level Maths and Further Maths, or you can find the full playlist here. These videos demonstrate a deeper cut of some of the most important ideas within A-level, so they are well worth a watch!
Playlist - Integration [This playlist is extended further in the Y13 section: Integration]
Integration as the limit of a sum (an alternative form of integration with which you should be familiar)
Interactive simulation:
Open the simulation here to explore the integral graphs of different functions (just tick the integral box on the right-hand side).
Can you predict what they will look like before showing the answer?
Extra fun! The Essence of Calculus - Integrals:
The Essence of Calculus - The fundamental theorem of calculus:
The Essence of Calculus - What does area have to do with slope?