NCERT Solutions for Class 12-science Maths Chapter 7 - Integrals

Updated NCERT Textbook Solutions Coming Soon!

Chapter 7 - Integrals Exercise Ex. 7.1

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

Solution 16

Solution 17

Solution 18

Solution 19

Solution 20

Solution 21

Solution 22

Chapter 7 - Integrals Exercise Ex. 7.2

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

Solution 16

Solution 17

Solution 18

Solution 19

Solution 20

Solution 21

Solution 22

Solution 23

Solution 24

Solution 25

Solution 26

Solution 27

Solution 28

Solution 29

Solution 30

Solution 31

Solution 32

Let sin x + cos x = t then (cos x - sin x) dx = dt

 

 

Solution 33

Put cos x - sin x = t then (- sin x - cos x)dx = dt

Solution 34

Solution 35

Solution 36

Solution 37

Solution 38

Solution 39

Chapter 7 - Integrals Exercise Ex. 7.3

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

Solution 16

Solution 17

Solution 18

Solution 19

Solution 20

Solution 21

Solution 22

Solution 23

Solution 24

Chapter 7 - Integrals Exercise Ex. 7.4

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

Solution 16

Solution 17

Solution 18

Solution 19

Solution 20

Solution 21

Solution 22

Solution 23

 

 

 

 

 

 

begin mathsize 12px style straight I subscript 2 equals integral fraction numerator 1 over denominator open parentheses straight x plus 2 close parentheses squared plus open parentheses square root of 6 close parentheses squared end fraction dx
space space space space space equals log open vertical bar straight x plus 2 plus square root of straight x squared plus 4 straight x plus 10 end root close vertical bar space space... left parenthesis 3 right parenthesis end style
 
 
 
Solution 24

Solution 25

begin mathsize 12px style straight I equals integral fraction numerator 1 over denominator square root of negative 4 open parentheses straight x squared minus begin display style fraction numerator 9 straight x over denominator 4 end fraction end style plus begin display style 81 over 64 end style minus begin display style 81 over 64 end style close parentheses end root end fraction dx end style

 

Chapter 7 - Integrals Exercise Ex. 7.5

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

Solution 16

Solution 17

Solution 18

Solution 19

Solution 20

Solution 21

Solution 22

Solution 23

Chapter 7 - Integrals Exercise Ex. 7.6

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

Solution 16

Solution 17

Solution 18

Solution 19

Solution 20

Solution 21

Solution 22

Solution 23

Solution 24

Chapter 7 - Integrals Exercise Ex. 7.7

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Chapter 7 - Integrals Exercise Ex. 7.8

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

 

Solution 6

Chapter 7 - Integrals Exercise Ex. 7.9

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

Solution 16


    
Solution 17

Solution 18

Solution 19

Solution 20

Solution 21

Solution 22

Chapter 7 - Integrals Exercise Ex. 7.10

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

 

 

 

Solution 10

Chapter 7 - Integrals Exercise Ex. 7.11

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14


Solution 15

Solution 16

Solution 17

Solution 18

Solution 19

Solution 20

Solution 21

Chapter 7 - Integrals Exercise Misc. Ex.

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

Solution 16

Solution 17

Solution 18

Solution 19

 
Solution 20

Solution 21

Solution 22

Solution 23

Solution 24

Solution 25

Solution 26

Solution 27

Solution 28

Solution 29

Solution 30

Solution 31

Solution 32

Solution 33

Solution 34

Solution 35

Solution 36

Solution 37

Solution 38

Solution 39

Solution 40

Solution 41

Solution 42

Solution 43

Solution 44