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.
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
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!
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:
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)
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?