1. IBSL Maths
Definite Integration
© Christine Crisp

2. 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

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

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

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

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

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

8. 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

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

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

11. 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

12. Exercises
1. Find
2. Find