Integrals

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

2. 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. Istituto Tecnico Industriale “A. Malignani”Udine Module: Integration N.Negrello I.T.I. Malignani - Udine

4. Istituto Tecnico Industriale “A. Malignani”Udine U.1.: Indefinite Integrals 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 N.Negrello I.T.I. Malignani - Udine

6. 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 U.2.: Lesson planning N.Negrello I.T.I. Malignani - Udine

8. 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 Cristina.Varsavsky@sci.monash.edu.au N.Negrello I.T.I. Malignani - Udine

9. EXERCISES Istituto Tecnico Industriale “A. Malignani”Udine We say: “ The integral be……. Or easily……. This is ……. 1) Complete   This is………..  f(x)dx abf(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. Istituto Tecnico Industriale “A. Malignani”Udine N.Negrello I.T.I. Malignani - Udine

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

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

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

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

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