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

2. Module C1 Module C2 AQA Edexcel MEI/OCR OCR
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3. The numbers on the integral sign are called the limits of integration
is a definite integral
The numbers on the integral sign are called the limits of integration

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

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

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

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

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

9. SUMMARY
The method for evaluating the definite integral is:
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

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

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

12. 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. Exercises
1. Find
2. Find

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

17. 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: