12M07�INTEGRALS
Differentiation
differentiation
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A
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B
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12M07.1�Integration as an anti-derivative
12M07.1 Integration as an anti-derivative
Learning Objectives
Introduction to Integration
Geometrical Meaning of Constant of Integration
Integration of some Standard Functions
Properties of Integration
12M07.0 Revision
Recall Test
12M07.1
CV1
Introduction to Integration
Derivative
Anti-Derivative
Integration
Integration – Inverse Process of Differentiation
B
derivative
Anti- derivative
Inverse
A
Activity
�Fill in the Blanks
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�Fill in the Blanks
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12M07.1
CV2
Nomenclature of Integration
Differentiation
Integration
Ex.
Integration of Standard Functions - Examples
���Here are some examples of derivatives , �try to find the anti-derivatives for same functions.�
12M07.1
CV3
Constant of Integration
Activity
Fill in the Blanks
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Pause the Video
(Time Duration : 02 Minutes)
Fill in the Blanks
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12M07.1
CV4
Geometrical Meaning of Constant of Integration
12M07.1
CV5
Integration of some Standard Functions
Activity
Fill in the Blanks
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Fill in the Blanks
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12M07.1
CV6
Properties of Integration
Constant Rule:
Addition/Subtraction Rule:
Ex.
12M07.1
CV7
Special Case of Integration
12M07.2
Integration by Substitution
Learning Objectives�
What is Integration by Substitution
�How to Calculate Integration by Substitution
12M07.2 – Integration by Substitution
12M07.2
CV 1
What is Integration by Substitution
Steps
Sol.
Ex.
(NCERT - Exercise 7.2 - Q1)
Ex.
Steps
Sol.
12M07.2
PSV 1
Q.
Sol.
(NCERT - Exercise 7.2 - Q29)
12M07.2
PSV 2
Sol.
Q.
(NCERT - Exercise 7.2 - Q. No. 37)
Sol.
Q.
(NCERT - Exercise 7.2 - Q37)
12M07.2
PSV 3
Q.
(NCERT - Exercise 7.2 – Q19)
Q.
Sol.
(NCERT - Exercise 7.2 – Q20)
12M07.2
PSV 4
Q.
Sol.
(NCERT - Exercise 7.2 - Q32)
Q.
Sol.
ConcepTest
Ready for a Challenge
Q.
Sol.
Pause the video
( Time Duration : 4 Minutes )
Ncert Ex. 7.2 Q.11
Q.
Sol.
(NCERT - Exercise 7.2 - Q11)
Q.
Sol.
Pause the video
( Time duration : 4 Minutes )
Q1
Q2
Q3
Q4
Q5
(NCERT - Exercise 7.2 - Q18)
(NCERT - Exercise 7.2 - Q25)
(NCERT - Exercise 7.2 - Q4)
(NCERT - Exercise 7.2 - Q9)
(NCERT - Exercise 7.2 - Q33)
Q1
Q2
Q3
Q4
Q5
Summary
3,8,16(I)
Reference Questions
NCERT Exercise 7.2 :
2,3,5,7,8,10,12,13,14,15,16,17,20,21,22,23,24,26,27,28,30,31,34,35,36,38,39
Work Book :
3,8,16(I)
12M07.2 – Integration by Substitution
Reference Questions
NCERT Exercise 7.2 :
Work Book :
2,3,5,7,8,10,12,13,14,15,16,17,20,21,22,23,24,26,27,28,30,31,34,35,36,38,39
3,8,16(I)
12M07.3
Integration using Trigonometric Identities
Learning Objectives�
When do we use Trigonometric Identities
�Integration using Trigonometric Identities
12M07.3 – Integration using Trigonometric Identities
Revision
Product to Sum Formulae
12M07.3
CV 1
When do we use Trigonometric Identities
12M07.3
CV 0
Trigonometric Identities
12M07.3
CV 2
Integration using Trigonometric Identities
Sol.
Ex.
Sol.
Ex.
Sol.
Ex.
12M07.3
PSV 1
Sol.
Q.
12M07.3
PSV 2
Q.
Sol.
(NCERT - Exercise 7.3 – Q11)
12M07.3
PSV 3
Sol.
Q.
(NCERT - Exercise 7.3 – Q12)
ConcepTest
Ready for a challenge
Sol.
Q.
Pause the Video
( Time Duration : 4 Minutes )
(NCERT - Exercise 7.3 – Q13)
Q1
Q2
Q3
Q4
Q5
(NCERT - Exercise 7.3 - Q10)
(NCERT - Exercise 7.3 – Q14)
(NCERT - Exercise 7.3 – Q3)
(NCERT - Exercise 7.3 – Q8)
(NCERT - Exercise 7.3 – Q18)
Q1
Q2
Q3
Q4
Q5
12M07.3 – Integration using Trigonometric Identities
Reference Questions
NCERT Exercise 7.3 :
Work Book :
1,2,4,5,6,7,9,15,16,17,19,20,21,22,23,24
12, 19(IV), 20(I)
Summary
3,8,16(I)
12M07.4
Integrals of Some Particular Functions
Learning Objectives
How to use Trigonometric Ratios
Integrals of Particular Functions
12M07.4 –Integrals of Some Particular Functions
12M07.4
CV 1
How to use Trigonometric Ratios
Using Standard form
Sol.
Ex.
Using Standard form
Sol.
Ex.
12M07.4
PSV 1
Sol.
Q.
(NCERT - Exercise 7.4 – Q4)
12M07.4
PSV 2
Sol.
Q.
(NCERT - Exercise 7.4 – Q3)
Using Standard form
Sol.
Ex.
Using Standard form
Sol.
Ex.
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Special forms of Integrals
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Special forms of Integrals
12M07.4
PSV 3
Sol.
Q.
12M07.4
PSV 4
Sol.
Q.
(NCERT - Exercise 7.4 - Q1)
ConcepTest 1
Ready for a Challenge
Sol.
Q.
Pause the video
( Time duration : 4 Minutes )
(NCERT - Exercise 7.4 – Q12)
12M07.4
CV 6
Integral of Particular Function
Solve this and find value of A and B
Sol.
Ex.
(NCERT - Exercise 7.4 – Q21)
ConcepTest 2
Ready for a Challenge
Sol.
Ex.
Pause the Video
( Time Duration : 5 Minutes )
(NCERT - Exercise 7.4 – Q22)
Q1
Q2
Q3
Q4
Q5
(NCERT - Exercise 7.4 – Q8)
(NCERT - Exercise 7.4 – Q10)
(NCERT - Exercise 7.4 – Q2)
(NCERT - Exercise 7.4 – Q5)
(NCERT - Exercise 7.4 – Q23)
Q1
Q2
Q3
Q4
Q5
Summary
3,8,16(I)
Summary
3,8,16(I)
12M07.4 – Integral of some Particular Functions
Reference Questions
NCERT Exercise 7.2 :
Work Book :
6,7,11,13,14,15,16,17,18,19,
20,24,25
9,10,17(II)
12M07.4 – Integral of some particular functions
Reference Questions
NCERT Exercise 7.2 :
Work Book :
6,7,11,13,14,15,16,17,18,19,
20,24,25
9,10,17(II)
Sol.
Q.
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Special forms of Integrals
�12M07.5�Integration by Partial Fractions�
Integration By Partial Fractions
Principle
12M07.5�CV1�When Denominator is in Factors Form
12M07.5�PSV01
12M07.5�CV2�When Denominator is in Square of Factors Form
Improper to proper rational functions
12M07.5�PSV02
Improper Function
12M07.5�PSV02
12M07.5�CV4�Derivation of formulae using partial fractions
12M07.6�Integration by Parts
Integration By Parts
Learning Objectives:
12M07.6�CV1�Anti-derivative of Product Rule
Principle
Substitution
Trigonometrical �Identities
Partial �Fractions
Anti-derivative of product rule
ILATE rule
I�
L��A��T��E
Inverse Function
Logarithm Function
Algebraic Function
Trigonometric Function
Exponential Function
I L A T E
12M07.6�PSV 01
I L A T E
12M07.6�PSV 02
12M07.6�PSV 03
12M07.6�CV3�Special Cases
12M07.6�PSV 04
�12M07.6�PSV 05
12M08�Definite Integral
12M08.1�Definite Integral: The limit of A Sum
Definite Integral: The Limit of A Sum
Learning Objectives:
Revision
If�
12M08.1�CV1�Definite Integral: The limit of A Sum
Principle
P
Q
R
S
The limit of the sum
12M08.1�PSV 01
12M08.2�Evaluation of Definite Integral
Evaluation of Definite Integral
Learning Objectives:
12M08.2�CV1�Evaluation for Area Function
Evaluation for Area Function
12M08.2�PSV01
12M08.2�PSV02
Evaluation of Definite Integral By substitution