1. N.Negrello I.T.I. Malignani - Udine
Integrals
N.Negrello I.T.I. Malignani - Udine

2. N.Negrello I.T.I. Malignani - Udine
Module: Integration
Where: 5^ class I.T.I. “A.Malignani” Udine
Time: 3 hours a week in the first term
Topics of the Module:
U1:Indefinite Integrals
U2:Integration techniques
Methodology
During the lessons students are asked to hypothesise, to discuss, to give opinions, to generalise and synthesise concepts. They are expected to use problem solving. Some lessons are done with the English teacher.
N.Negrello I.T.I. Malignani - Udine

3. Module: Integration Istituto Tecnico Industriale “A. Malignani” Udine
Time Table
Units
Time
Indefinite integral Unit 1
Whole class teaching;
Use EPSILON
Test for monitoring understanding
Scientific language
Vocabulary reinforcement
3 hours
2 hours
1 hour
1 hour with the English teacher
Integration techniques Unit 2
Final test
4 hours
Revising with EPSILON
2 hour
TOTAL
18 hours
N.Negrello I.T.I. Malignani - Udine

4. N.Negrello I.T.I. Malignani - Udine
Indefinite Integrals
Istituto Tecnico Industriale “A. Malignani” Udine
What to do:
Graphic identification of functions and anti-derivatives
Apply the properties of indefinite integrals
Aims
What to know :
The definition of the set of anti-derivatives of a function
The relation between integration and derivation
The definition of a definite integral
The difference between indefinite and definite integral
Properties of indefinite integrals
Integration vocabulary
N.Negrello I.T.I. Malignani - Udine

5. U.1.:
Lesson planning
Istituto Tecnico Industriale “A. Malignani” Udine
Contents
Definition of indefinite integral
Relation of integration and derivation
Recognise this relation in different contexts
Cognitive Process
Working out concepts and links.
Asking for explanations
Improving vocabulary
Teacher activity
Whole class teaching
Interactive teaching
Problem solving
Learning support
EPSILON
B/B
Total Time
6 hours + 1 hour (test)
N.Negrello I.T.I. Malignani - Udine

6. N.Negrello I.T.I. Malignani - Udine
U.2.: Integration Techniques
Istituto Tecnico Industriale “A. Malignani” Udine
What to know:
Rules of substitution technique
Rules of integration by part
Rules of integration of rational functions
Aims
What to Do:
Apply integration rules
N.Negrello I.T.I. Malignani - Udine

7. Istituto Tecnico Industriale “A. Malignani” Udine
Lesson planning
Contents
Integration by substitution
Integration by part
Integration of rational functions
Integration of some irrational functions
Cognitive Process
Applying rules
Asking for explanations
Teacher activity
Whole class teaching
Interactive teaching
Learning support
EPSILON
B/B
Total Time
8 hours + 1 hour (test)
N.Negrello I.T.I. Malignani - Udine

8. N.Negrello I.T.I. Malignani - Udine
Istituto Tecnico Industriale “A. Malignani” Udine
Examples of the use of EPSILON and of
monitoring / understanding
exercises
Epsilon = software multimedia Monach University – Melbourne- Australia Cristina Varsavsky
N.Negrello I.T.I. Malignani - Udine

9. N.Negrello I.T.I. Malignani - Udine
EXERCISES
Istituto Tecnico Industriale “A. Malignani” Udine
We say: “ The integral be…….
Or easily…….
This is …….
1) Complete  
This is………..
 f(x)dx
ab f(x)dx
We’ll read this as integral be…..
Or easily……..
 2) Fill in the gaps
Integration is the…….. process of differentiation. In order to …….. with confidence it is helpful to have a good knowledge of ……….. techniques, because when ……… a function, we often try to figure out what has been ……… to give that function.For ……….integration, …….. are given and a numerical value obtained. When there are no limits, the integration is known as ………., and it is necessary to include the integration …….., usually written C.
N.Negrello I.T.I. Malignani - Udine

10. N.Negrello I.T.I. Malignani - Udine
Istituto Tecnico Industriale “A. Malignani” Udine
N.Negrello I.T.I. Malignani - Udine

11. N.Negrello I.T.I. Malignani - Udine
Istituto Tecnico Industriale “A. Malignani” Udine
N.Negrello I.T.I. Malignani - Udine

12. N.Negrello I.T.I. Malignani - Udine
Istituto Tecnico Industriale “A. Malignani” Udine
N.Negrello I.T.I. Malignani - Udine

13. N.Negrello I.T.I. Malignani - Udine
Istituto Tecnico Industriale “A. Malignani” Udine
N.Negrello I.T.I. Malignani - Udine

14. N.Negrello I.T.I. Malignani - Udine
Istituto Tecnico Industriale “A. Malignani” Udine
N.Negrello I.T.I. Malignani - Udine

15. N.Negrello I.T.I. Malignani - Udine
Istituto Tecnico Industriale “A. Malignani” Udine
N.Negrello I.T.I. Malignani - Udine