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# RD Sharma Solution for Class 12 Science Mathematics Chapter 20 - Definite Integrals

Our RD Sharma Textbook Solutions are considered extremely helpful for solving the tough questions which are asked in the CBSE Class 12 exam. TopperLearning Textbook Solutions are compiled by subject experts. Herein, you can find all the answers to the textbook questions for Chapter 20 - Definite Integrals.

All our solutions are created in accordance with the latest CBSE syllabus, and they are amended from time to time to provide the most relevant answers. Our free RD Sharma Solutions for CBSE Class 12 Mathematics will strengthen your fundamentals in Mathematics and will help you in your attempts to score more marks in the final examination. CBSE Class 12 students can refer to our solutions any time — while doing their homework and while preparing for the exam.

Exercise/Page

## RD Sharma Solution for Class 12 Science Mathematics Chapter 20 - Definite Integrals Page/Excercise 20.1

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

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

Solution 45

Solution 46

Solution 47

Solution 48

Solution 49

Solution 50

Solution 51

Solution 52

Solution 53

Solution 54

Solution 55

Let cosx =u , Then

Hence

Solution 56

Solution 57

Solution 58

Solution 59

Given :

Solution 60

Solution 61

Solution 62

Solution 63

We know , By reduction formula

For n=2

For n=4

Hence

Note: Answer given at back is incorrect.

Solution 64

Using Integration By parts

Solution 65

Solution 66

Note: Answer given in the book is incorrect.

Solution 67

=(1/4)log(2e)

## RD Sharma Solution for Class 12 Science Mathematics Chapter 20 - Definite Integrals Page/Excercise 20.2

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

Using Integration By parts

Hence

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

Solution 45

Solution 46

Solution 47

Solution 48

Solution 49

Solution 50

Solution 51

Solution 52

Solution 53

Solution 54

Solution 55

Solution 56

Solution 57

Solution 58

Solution 59

Solution 60

Solution 61

Solution 62

## RD Sharma Solution for Class 12 Science Mathematics Chapter 20 - Definite Integrals Page/Excercise 20.3

Solution 1(i)

Solution 1(ii)

Solution 1(iii)

Solution 2

Solution 3

Solution 4

Solution 5

2x+3 is positive for x>-1.5 . Hence

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

For

Using Integration By parts

For

Using Integration By parts

Solution 22

Solution 23

Solution 24

Solution 25

Solution 27

[x]=0 for 0

Solution 28

Solution 26

## RD Sharma Solution for Class 12 Science Mathematics Chapter 20 - Definite Integrals Page/Excercise 20.4A

Solution 1

We know

Hence

We know

If

Then also

Hence

Solution 2

We know

Hence

If

Then

Solution 3

We know

Hence

If

Then

So

Solution 4

We know

Hence

If

Then

Hence

Solution 5

We know

Hence

If

Then

So

We know

If f(x) is even

If f(x) is odd

Here

f(x) is even, hence

Note: Answer given in the book is incorrect.

Solution 6

We know

Hence

If

Then

So

Solution 7

We know

Hence

If

Then

So

Solution 8

We know

Hence

If

Then

So

Note: Answer given in the book is incorrect.

Solution 9

If f(x) is even

If f(x) is odd

Here

is odd and

is even. Hence

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

Solution 16

Solution 1

Solution 2

Solution 3

B

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

Hence

Solution 20

Solution 21

Now

Let cosx=t

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

We know

Also here

So

Hence

Solution 39

Solution 40

Solution 41

Solution 42

Solution 43

Solution 44

Solution 45

Solution 46

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

Solution 45

Solution 46

Solution 47

Solution 48

Solution 49

Solution 50

Solution 51

Solution 52

Solution 53

Solution 54

Solution 55

Solution 56

Solution 57

Solution 58

Solution 59

Solution 60

Solution 61

Solution 62

Solution 63

Solution 64

Solution 65

Solution 66

Solution 67

Solution 68

Solution 69

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

## RD Sharma Solution for Class 12 Science Mathematics Chapter 20 - Definite Integrals Page/Excercise MCQ

Solution 1

Correct option: (d)

Solution 2

Correct option: (c)

Solution 3

Correct option: (a)

Solution 4

Correct option: (c)

Solution 5

Correct option:(c)

Solution 6

Correct option: (b)

Solution 7

Correct option: (a)

Solution 8

Correct option: (d)

Solution 9

Correct option: (b)

Solution 10

Solution 11

Correct option: (a)

Solution 12

Correct option:(c)

Solution 13

Correct option: (a)

Solution 14

Correct option: (a)

Solution 15

Correct option:(a)

Solution 16

Correct option:(a)

Solution 17

Correct option:(b)

Solution 18

Correct option: (b)

Solution 19

Correct option: (a)

Solution 20

Correct option: (b)

Solution 21

Correct option:(b)

Solution 22

Correct option: (b)

Solution 23

Correct option: (c)

Solution 24

Correct option: (b)

Solution 25

Correct option: (b)

Solution 26

Correct option:(c)

Solution 27

Correct option: (b)

Solution 28

Correct option: (d)

Note: Question is modified.

Solution 29

Correct option: (c)

Solution 30

Correct option:(a)

Solution 31

Correct option:(d)

Solution 32

Correct option: (d)

Solution 33

Correct option:(c)

Solution 34

Correct option:(d)

Solution 35

Correct option: (c)

Solution 36

Correct option: (a)

Solution 37

Correct option:(d)

Solution 38

Correct option: (c)

Solution 39

Correct option: (d)

Solution 40

Correct option: (b)

Solution 41

Correct option: (c)

Solution 42

Correct option: (c)

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 n

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

Solution 45

## Browse Study Material

TopperLearning provides step-by-step solutions for each question in each chapter in the RD Sharma textbook for class 9. Access the CBSE Class 9 Mathematics Chapter 20 - Definite Integrals for free. The textbook questions have been solved by our subject matter experts to help you understand how to answer them. Our RD Sharma Textbook Solutions will help you to study and revise, and you can easily clear your fundamentals of Chapter 20 - Definite Integrals.

# Text Book Solutions

CBSE XII Science - Mathematics

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