6 The contents of this study and revision guide are designed to guide you through to success in the Pure Mathematics component of the WJEC Mathematics for A2 level: Pure examination. It has been written by an experienced author and teacher and edited by a senior subject expert. This book has been written speciϐically for the WJEC A2 course you are taking and includes everything you need to know to perform well in your exams. Knowledge and Understanding 149 Introduction You came across integration in Topic 8 of the AS Pure 1 course. Integration is the opposite of differentiation, so to integrate a term, you add one to the index and then divide by the new index. With indefinite integration you must remember to include a constant of integration and with definite integration you substitute in numbers. Definite integrals represent the area under the curve. As you will be building on the material from Topic 8 of the AS Pure course, you should look over that material before starting this topic. This topic covers the following: 7.1 Integration of x n ( n ≠ Ϋ 1), e kx , 1 x , sin kx , cos kx 7.2 Integration of ( ax + b ) n ( n ≠ Ϋ 1), e ax + b , 1 ax + b , sin( ax + b ), cos( ax + b ) 7.3 Using definite integration to find the area between two curves 7.4 Using integration as the limit of a sum 7.5 Integration by substitution and integration by parts 7.6 Integration using partial fractions 7.7 Analytical solution of first order differential equations with separable variables 11/09/2018 12:16 Topics start with a short list of the material covered in the topic and each topic will give the underpinning knowledge and skills you need to performwell in your exams. The knowledge section is kept fairly short, leaving plenty of space for detailed explanation of examples. Pointers will be given to the theory, examples and questions that will help you understand the thinking behind the steps. You will also be given detailed advice when it is needed. The following features are included in the knowledge and understanding sections: • Grade boosts are tips to help you achieve your best grade by avoiding certain pitfalls which can let students down.