1. 25: Definite Integration © Christine Crisp “Teach A Level Maths” Vol. 1: AS Core Modules

2. Definite Integration Module C1 AQA Edexcel OCR MEI/OCR Module C2 "Certain images and/or photos on this presentation are the copyrighted property of JupiterImages and are being used with permission under license. These images and/or photos may not be copied or downloaded without permission from JupiterImages"

3. Definite Integration The numbers on the integral sign are called the limits of integration e.g.1 is a definite integral

4. Definite Integration  Find the indefinite integral but omit C The definite integration results in a value. Evaluating the Definite Integral e.g.1

5. Definite Integration e.g.1 The definite integration results in a value. Evaluating the Definite Integral  Draw square brackets and hang the limits on the end

6. Definite Integration The definite integration results in a value. Evaluating the Definite Integral  Replace x with the top limit the bottom limit e.g.1

7. Definite Integration Evaluating the Definite Integral  Subtract and evaluate The definite integration results in a value. e.g.1

8. Definite Integration Evaluating the Definite Integral The definite integration results in a value. So, e.g.1

9. Definite Integration SUMMARY  Find the indefinite integral but omit C  Draw square brackets and hang the limits on the end  Replace x with the top limit the bottom limit  Subtract and evaluate The method for evaluating the definite integral is:

10. Definite Integration Evaluating the Definite Integral e.g. 2 Find Solution: Indefinite integral but no C

11. Definite Integration Evaluating the Definite Integral e.g. 2 Find Solution: Substitute for x : top limit minus bottom limit Simplify

12. Definite Integration Evaluating the Definite Integral In this example, if we can’t use a calculator, we can save time by collecting terms from both brackets. We must be very careful with the signs

13. Definite Integration Exercises 1. Find 2. Find

14. Definite Integration

15. The following slides contain repeats of information on earlier slides, shown without colour, so that they can be printed and photocopied. For most purposes the slides can be printed as “Handouts” with up to 6 slides per sheet.

16. Definite Integration Evaluating the Definite Integral The definite integration results in a value. So, e.g.1

17. Definite Integration SUMMARY  Find the indefinite integral but omit C  Draw square brackets and hang the limits on the end  Replace x with the top limit the bottom limit  Subtract and evaluate The method for evaluating the definite integral is: