Integration - A. Malignani

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
Istituto Tecnico Industriale
“A. Malignani”
Udine
Module:
Integration
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
Whole class teaching;
Use EPSILON
Test for monitoring understanding
Scientific language
Vocabulary reinforcement
Final test
4 hours
2 hours
1 hour
1 hour with the English teacher
1 hour
Revising with EPSILON
2 hour
TOTAL
18 hours
N.Negrello I.T.I. Malignani - Udine
U.1.:
Indefinite Integrals
Istituto Tecnico Industriale
“A. Malignani”
Udine
What to do:
Graphic identification of functions
and anti-derivatives
Aims
Apply the properties of indefinite
integrals
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
Istituto Tecnico Industriale
“A. Malignani”
Udine
U.1.:
Lesson planning
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
U.2.:
Integration Techniques
Istituto Tecnico Industriale
“A. Malignani”
Udine
What to know:
Aims
Rules of substitution technique
Rules of integration by part
Rules of integration of rational functions
What to Do:
Apply integration rules
N.Negrello I.T.I. Malignani - Udine
U.2.:
Lesson planning
Istituto Tecnico Industriale
“A. Malignani”
Udine
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
Total Time
EPSILON
B/B
8 hours + 1 hour (test)
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
[email protected]
N.Negrello I.T.I. Malignani - Udine
EXERCISES
Istituto Tecnico Industriale
“A. Malignani”
Udine
We say: “ The integral
be…….
1) Complete
This is………..
 f(x)dx
Or easily…….
This is …….
a f(x)dx
b
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
Istituto Tecnico Industriale
“A. Malignani”
Udine
N.Negrello I.T.I. Malignani - Udine
Istituto Tecnico Industriale
“A. Malignani”
Udine
N.Negrello I.T.I. Malignani - Udine
Istituto Tecnico Industriale
“A. Malignani”
Udine
N.Negrello I.T.I. Malignani - Udine
Istituto Tecnico Industriale
“A. Malignani”
Udine
N.Negrello I.T.I. Malignani - Udine
Istituto Tecnico Industriale
“A. Malignani”
Udine
N.Negrello I.T.I. Malignani - Udine
Istituto Tecnico Industriale
“A. Malignani”
Udine
N.Negrello I.T.I. Malignani - Udine