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VINH LONG HIGH SCHOOL
WELCOME ALL TEACHERS TO OUR CLASS 12X3
TEACHER : TRAN TRAN HUYNH

VINH LONG DEPARTMENT OF EDUCATION AND TRAINING
VINH LONG HIGH SCHOOL


REVIEW OF INTEGRALS
TEACHER : TRAN TRAN HUYNH
SUBJECT : MATHS
TRAN TRAN HUYNH - VINH LONG HIGH SCHOOL
ANALYSIS 12
MAJOR CONTENT
METHOD OF
INTEGRATION
PROPERTY
DEFINITION
TEACHING FESTIVAL VINH LONG PROVINCE
2/ Method of change of variables( 2 types):
3/ Method of intergration by parts:
1/ Simple integration uses directly the primitive properties and table .
EXERCISE 1:
Compute the following integrals :
TRAN TRAN HUYNH - VINH LONG HIGH SCHOOL
ANALYSIS 12
EXERCISE 2:
Compute the following integrals :
TRAN TRAN HUYNH - VINH LONG HIGH SCHOOL
ANALYSIS 12
REINFORCE KNOWLEDGE
MAJOR CONTENT:
* Definition and properties of integrals.
* Simple integration uses directly the primitive properties and table .
HOMEWORK:
* Integration by changing of variables.
*Do all the homework in the handouts .
* Preparation :Calculate integration and solve geometric application of integrals .
* Integration by parts
TRAN TRAN HUYNH - VINH LONG HIGH SCHOOL
ANALYSIS 12
THANK FOR
YOUR ATTEND!
THE LESSON IS OVER
Some signs to use the method of integration by parts:
Note : “ L.P.T.E”
L(logs),P(polynomial),T(trionometry),E(exponential)
TRAN TRAN HUYNH - VINH LONG HIGH SCHOOL
ANALYSIS 12
* Let :
* We have :
* New integral calculation:
* Take the differential of 2 sides :
TRAN TRAN HUYNH - VINH LONG HIGH SCHOOL
ANALYSIS 12
Fill in the blank to change the appropriate variable of integrals .
TRAN TRAN HUYNH - VINH LONG HIGH SCHOOL
ANALYSIS 12
Let:
Therefore:
Solution:
We have:
Letting: