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Edited By Kuldeep Maurya | Updated on Jan 24, 2022 12:47 PM IST

The RD Sharma books are the most prescribed solution materials by the CBSE board schools to their students. It helps them in solving sums that are complicated, and they can recheck their answers effortlessly. Moreover, in class 12, chapter 18 in mathematics has Revision Exercise (RE) for the students to practice better in this chapter. The questions given in this are challenging to solve; hence, they can use the RD Sharma Class 12th RE book as a reference.

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Chapter 18 - Indefinite Integrals - Ex-18.1

Indefinite Integrals Exercise Revision Exercise Question 1

Hint:

Do Rationalization

we have,

Indefinite Integrals Exercise Revision Exercise Question 2

Hint:

Use the formula

Indefinite Integrals Exercise Revision Exercise Question 3

Hint:

Use power rule for integration.

Indefinite Integrals Exercise Revision Exercise Question 4

Hint:

Separate the terms and integrate

Indefinite Integrals Exercise Revision Exercise Question 5

Hint:

Use partial function method.

using partial function

now,

Indefinite Integrals Exercise Revision Exercise Question 7

Hint:

Do rationalization and then use trigonometry identities.

On rationalising,

Indefinite Integrals Exercise Revision Exercise Question 9

Hint:

Use trigonometry identity.

Indefinite Integrals Exercise Revision Exercise Question 10

Hint:

Use trigonometric identities and integrate it by parts.

Indefinite Integrals Exercise Revision Exercise Question 11

Hint:

You must know about trigonometric identities.

Indefinite Integrals Exercise Revision Exercise Question 12

Hint:

Let the term and derivate it and then integrate it.

Indefinite Integrals Exercise Revision Exercise Question 13

Hint:

Let the denominator and then integrate the equation.

Indefinite Integrals Exercise Revision Exercise Question 15

Hint:

We must know about substitution formula to integrate.

Let

Differentiate it with respect to x

Indefinite Integrals Exercise Revision Exercise Question 16

Hint:

Do integration by separation.

Differentiate it with respect to x

Indefinite Integrals Exercise Revision Exercise Question 17

Use partial fraction method.

use partial fraction

So,

Indefinite Integrals Exercise Revision Exercise Question 18

Hint:

Use substitution method.

Indefinite Integrals Exercise Revision Exercise Question 19

Hint:

Use trigonometric identities and substitution method of integration.

Solution:

Let

Indefinite Integrals Exercise Revision Exercise Question 20

Hint:

Use the formula

Indefinite Integrals Exercise Revision Exercise Question 21

Hint:

To solve this equation we will use trigonometry method.

Indefinite Integrals Exercise Revision Exercise Question 22

Hint:

To solve this equation we use partial function method.

Indefinite Integrals Exercise Revision Exercise Question 23

Hint:

To solve this equation we use sin x formula and substitute method.

Let

Indefinite Integrals Exercise Revision Exercise Question 24

Hint:

To solve the statement we have to use formula such as sin(A-B).

Indefinite Integrals Exercise Revision Exercise Question 25

Hint:

To solve this statement we have to convert cos into tan.

Indefinite Integrals Exercise Revision Exercise Question 26

Hint:

To solve the statement we have to use formula like sin x and 1+cos x

Indefinite Integrals Exercise Revision Exercise Question 27

Hint:

To solve the equation we will use substitution method.

Indefinite Integrals Exercise Revision Exercise Question 28

Hint:

To solve this statement we have to change tan into sec form.

Indefinite Integrals Exercise Revision Exercise Question 29

Hint:

To solve this statement we have to change tan into sec and then their formula.

Indefinite Integrals Exercise Revision Exercise Question 30

Hint:

To solve this statement we have to change tan into sec and then use formula such tan²x.

Indefinite Integrals Exercise Revision Exercise Question 31

Hint:

To solve the given statement split the given term into

Indefinite Integrals Exercise Revision Exercise Question 32

Hint:

To solve the given statement we will split into

Indefinite Integrals Exercise Revision Exercise Question 33

Hint:

To solve the statement we will use partial fractions

On equating the coeffiecients of

On equating the coeffiecients of

On equating the constants :

Thus,

Indefinite Integrals Exercise Revision Exercise Question 34

To solve the statement we have to put root statement to

Indefinite Integrals Exercise Revision Exercise Question 35

Hint:

To solve the statement we will suppose x in term of t.

Indefinite Integrals Exercise Revision Exercise Question 36

Hint:

To solve this statement we have to suppose or assume sin x and cos x as v and dv.

Indefinite Integrals Exercise Revision Exercise Question 37

Hint:

To solve the statement we will convert cos into sin and use some formula of 2sin(A+B) and 2sin(A-B)

put

Indefinite Integrals Exercise Revision Exercise Question 38

Hint:

To solve the statement we have to convert sin x into cos x.

Let cosx= t

Indefinite Integrals Exercise Revision Exercise Question 39

Hint:

To solve the statement we have to convert cos term in sin

Indefinite Integral Exercise Rivision Exercise Question 66

Answer :Hint: To solve the given solution we multiply and divide the given statement with sin x.

Given :

Solution :

Indefinite Integrals Exercise Revision Exercise Question 40

Hint:

To solve this equation we have to suppose sin x in term of t and cos x into 2t.

Indefinite Integrals Exercise Revision Exercise Question 41

Hint:

In this statement we have to convert sin in term of tan.

Indefinite Integral Exercise Rivision Exercise Question 67

Answer :Hint : To solve the given statement we will use partial fraction rule.

Given :

Solution :

On solving,

Indefinite Integrals Exercise Revision Exercise Question 42

Hint:

In this statement we have to assume x as asecθ.

Indefinite Integrals Exercise Revision Exercise Question 43

Hint:

In this statement we assume x as atanθ.

Indefinite Integrals Exercise Revision Exercise Question 44

Hint:

To solve this equation we will use split term method.

Indefinite Integrals Exercise Revision Exercise Question 46

Hint:

To solve this statement we have to do whole square method.

Indefinite Integrals Exercise Revision Exercise Question 47

Hint:

In this equation we have to make whole square statement from quadratic equation.

Indefinite Integrals Exercise Revision Exercise Question 48

Hint:

To solve this statement we have to use standard formula.

Indefinite Integrals Exercise Revision Exercise Question 49

Hint:

To solve this statement we have to convert cosec into sin and then we apply standard formula.

sin x = t ,

dt = cos x dx

Indefinite Integrals Exercise Revision Exercise Question 52

Hint:

To solve this equation we have to do differentiation method.

Take 5/2 common from numerator and add and subtract 9,

Indefinite Integrals Exercise Revision Exercise Question 53

ùTo solve this equation we have to take x = u².

Indefinite Integrals Exercise Revision Exercise Question 54

Hint:

To solve this question we have to assume that x as sin²θ

Indefinite Integrals Exercise Revision Exercise Question 55

Hint:

To solve this equation we have to suppose denominator as t.

Indefinite Integrals Exercise Revision Exercise Question 56

Hint:

To solve this statement we have to evaluate the team by partial fraction.

Dividing cos²x with numerator and denominator.

Indefinite Integrals Exercise Revision Exercise Question 57

Hint:

To solve this statement we have to divide numerator and denominator by cos²θ.

Dividing numerator and denominator by cos²x.

Indefinite Integrals Exercise Revision Exercise Question 58

Hint:

To solve this equation, we have to use standard method form.

On solving (1) and (2),

Indefinite Integrals Exercise Revision Exercise Question 59

Hint:

To solve this equation we have to take sin²x common and also use sin2x formula.

Indefinite Integrals Exercise Revision Exercise Question 60

Hint:

To solve this statement we have to use formula of sin θ+ 2cos θ and also substitute method.

Indefinite Integrals Exercise Revision Exercise Question 61

Hint :

To solve this given statement split the x? term to (x?)² then put x? equal to t.

Indefinite Integrals Exercise Revision Exercise Question 62

Hint:

To solve the given statement we will take

Indefinite Integrals Exercise Revision Exercise Question 63

Hint:

To solve this given statement we will write cos²x in terms of sin²x

Indefinite Integrals Exercise Revision Exercise Question 65

Hint:

To solve the above equation we will write sin x as * ***Given:****Solution: **** **** **** **

Indefinite Integrals Exercise Revision Exercise Question 69

Hint:

To solve the given statement write * ***Given:****Solution:**

Indefinite Integrals Exercise Revision Exercise Question 70

Hint:

To solve the given statement split the sec? x into sec² x sec²x then apply the formula.

Indefinite Integrals Exercise Revision Exercise Question 71

Hint:

To solve the given question we will split the cosec? 2x into cosec² 2x cosec² 2x.

Indefinite Integrals Exercise Revision Exercise Question 72

Hint:

To solve the given statement multiply and divide the equation by sin x.

Indefinite Integrals Exercise Revision Exercise Question 73

Hint:

To solve the given statement we will write

Indefinite Integrals Exercise Revision Exercise Question 74

Hint:

To solve the given statement multiply and divide the equation by a +x.

Indefinite Integrals Exercise Revision Exercise Question 75

Hint:

To solve the given solution we will use the partial fraction.

Indefinite Integrals Exercise Revision Exercise Question 76

Hint:

To solve the given statement we will split sin 5x into sin? x sin x.

Indefinite Integrals Exercise Revision Exercise Question 77

Hint:

to solve the given statement we will split cos? x into cos? x cos x then put cos? x = (1-sin²x)².

Indefinite Integrals Exercise Revision Exercise Question 78

Hint:

To solve the given equation we have to split the sin? x term in sin? x.sin² x.

Indefinite Integrals Exercise Revision Exercise Question 79

Hint:

To solve the given statement divide the numerator and denominator by cos²x.

Indefinite Integrals Exercise Revision Exercise Question 80

Hint:

To solve the given equation we have to split sec? x into sec? x sec² x.

Indefinite Integrals Exercise Revision Exercise Question 81

Hint:

You must know about integration of tan x & sec x.

Indefinite Integrals Exercise Revision Exercise Question 82

Hint:

You must know about the integration of tan x & sec x.

Indefinite Integrals Exercise Revision Exercise Question 83

Hint:

You must know about integration of sec x & cosec x.

Indefinite Integrals Exercise Revision Exercise Question 84

Hint:

You must know about integration of

Indefinite Integrals Exercise Revision Exercise Question 86

Hint:

You must know about how to solve integration.

Indefinite Integrals Exercise Revision Exercise Question 87

Hint:

You must know about how to solve integration.

Indefinite Integrals Exercise Revision Exercise Question 88

Hint:

You must know about formula of

Indefinite Integrals Exercise Revision Exercise Question 89

Hint:

You have to find value of A & B.

A + B = 0 , -2A = 1

Indefinite Integrals Exercise Revision Exercise Question 90

Hint:

You must have to know about integration method.

Indefinite Integrals Exercise Revision Exercise Question 91

Hint:

You must know about integration of cos2x.

Indefinite Integrals Exercise Revision Exercise Question 92

Hint: You must know about integration of logx.

Indefinite Integrals Exercise Revision Exercise Question 93

Hint:

You must know about integration of log.

put value of t

Indefinite Integrals Exercise Revision Exercise Question 94

Hint:

You must know about integration of sec x & tan x.

Indefinite Integrals Exercise Revision Exercise Question 96

Hint:

You must know about integration of I and II.(ILATE)

Indefinite Integrals Exercise Revision Exercise Question 98

Hint:

You must know about integration of e?

Resubs. t=logx,

Indefinite Integrals Exercise Revision Exercise Question 99

Hint:

You must know about ILATE

Indefinite Integrals Exercise Revision Exercise Question 100

Hint:

You must know about the log formula of integration.

Indefinite Integrals Exercise Revision Exercise Question 102

Hint: to solve this question we have to use differentiate method

Indefinite Integrals Exercise Revision Exercise Question 103

Hint: to solve this question we have to use substitute method

Indefinite Integrals Exercise Revision Exercise Question 104

Hint: to solve this equation we have to solve this by splitting the team

Indefinite Integrals Exercise Revision Exercise Question 105

Hint: to solve this equation, we have to assume u as

Indefinite Integrals Exercise Revision Exercise Question 106

Hint: to solve this equation we have to do with differentiate method.

Indefinite Integrals Exercise Revision Exercise Question 107

Hint: to solve this we have to put in team of t

Indefinite Integrals Exercise Revision Exercise Question 108

Hint: in this equation we will us ILATE method and then differentiate the terms

Indefinite Integrals Exercise Revision Exercise Question 109

Hint: to solve this equation we have to use Byparts method

Indefinite Integrals Exercise Revision Exercise Question 110

Hint: to solve the question we have to use ILATE method

Indefinite Integrals Exercise Revision Exercise Question 111

Hint: to solve this equation we have to useByparts equation;

Solution: Let

Indefinite Integrals Exercise Revision Exercise Question 112

Hint: to solve this question we will presume x as

Indefinite Integrals Exercise Revision Exercise Question 115

Hint: to solve this equation, we have to convert equation into trigonometric formulaes

Indefinite Integrals Exercise Revision Exercise Question 113

Hint: to solve this statement we will assume sin as tan

Indefinite Integrals Exercise Revision Exercise Question 114

To solve this question we will use ILATE Method

Indefinite Integrals Exercise Revision Exercise Question 116

Hint: to solve this statement we will suppose x as

Indefinite Integrals Exercise Revision Exercise Question 117

Hint: to solve this equation, we have to assume x as and then do byparts method**Given: ****Soluton: **Let

Indefinite Integrals Exercise Revision Exercise Question 118

Hint: to solve this equation, we have to assume 2x as t

Indefinite Integrals Exercise Revision Exercise Question 119

Hint : To solve this equation we have to use differentiation method

Indefinite Integrals Exercise Revision Exercise Question 12

Hint: to solve this equation, we have to break the

Indefinite Integrals Exercise Revision Exercise Question 121

Hint: using integration by parts

Explanation

Put

Indefinite Integrals Exercise Revision Exercise Question 122

Hint: you must know the steps to integrate by partial function

Explanation: let

Multiplying by

Putting x=1

Putting x=-1

Putting x=0

Putting x=2

Adding (i) and (ii)

Put in (1)

Indefinite Integrals Exercise Revision Exercise Question 123

Hint: using partial function

Explanation let

Multiplying by

Putting x=1

Putting x=-1

Putting x=0

Put in (1)

Where

By (2), we get

Indefinite Integrals Exercise Revision Exercise Question 124

Hint: using partial function

Explanation: let

Multiplying by

Indefinite Integrals Exercise Revision Exercise Question 125

Hint: Using

Indefinite Integrals Exercise Revision Exercise Question 126

Hint: using partial fraction

Explanation let

Multiply by

Indefinite Integrals Exercise Revision Exercise Question 127

Hint: You must know the derivatives and integration of sinx and cosx

Explanation:

Let

Indefinite Integrals Exercise Revision Exercise Question 128

Hint: using partial fraction

Explanation: let

Multiplying by :

Putting x=-1

Indefinite Integrals Exercise Revision Exercise Question 129

Let

Indefinite Integrals Exercise Revision Exercise Question 130

Hint: using partial fraction and

Revising the proper set of questions is essential. And class 12, mathematics chapter 18 consists of around 32 exercises. This brings to the point that students might forget what they have learned in the first exercise when they reach the 32nd one. Therefore, it becomes essential to revise the previous portion before jumping to the next chapter.

The RE portion consists of 130 questions with subparts to be answered. These questions come under the concept of evaluating the integrals, Solutions on indefinite integral, Integration by parts, Questions on Fundamental integration formulas, Integration of trigonometric functions.

The students will be required to work out all the sums to have a general idea of the entire chapter. RD Sharma Solution In such instances, recheck or searching for the correct answers become hectic. Hence, the RD Sharma Class 12 Chapter 18 RE solution book can help them out.

This solution book follows the NCERT pattern and can be used by the CBSE board students without hesitation. Instead of picking sums from every exercise separately, this combination of questions will benefit the students by making their work effortless. Hence, you can have a better practice method and an authorized material to refer to the accurate solutions when you have the RD Sharma Class 12th RE book.

Practicing the sums listed in the Revision exercise gives a general idea of all the concepts, formulas, and methods that you have learned in this chapter. You can use the Class 12 RD Sharma Chapter 18 RE Solution material to look out for clarifications or answers. Solving the sums in all the 32 exercises at once will give you a higher level of confidence to face any integration questions. Hence, the RD Sharma Class 12th RE book plays a significant role in making you exam-ready by all means.

The best part of the RD Sharma Class 12 Solutions Indefinite Integrals RE book is that you are not required to pay any money or other monetary charges. All the RD Sharma books are available for free of cost on the Career 360 website. In addition, many students of previous batches have benefitted by using the RD Sharma Class 12 Solutions Chapter 18 RE material for reference. Download your own set of RD Sharma solution books from the Career 360 website.

- Chapter 1 - Relations
- Chapter 2 - Functions
- Chapter 3 - Inverse Trigonometric Functions
- Chapter 4 - Algebra of Matrices
- Chapter 5 - Determinants
- Chapter 6 - Adjoint and Inverse of a Matrix
- Chapter 7 - Solution of Simultaneous Linear Equations
- Chapter 8 - Continuity
- Chapter 9 - Differentiability
- Chapter 10 - Differentiation
- Chapter 11 - Higher Order Derivatives
- Chapter 12 - Derivative as a Rate Measurer
- Chapter 13 - Differentials, Errors and Approximations
- Chapter 14 - Mean Value Theorems
- Chapter 15 - Tangents and Normals
- Chapter 16 - Increasing and Decreasing Functions
- Chapter 17 - Maxima and Minima
- Chapter 18 - Indefinite Integrals
- Chapter 19 - Definite Integrals
- Chapter 20 - Areas of Bounded Regions
- Chapter 21 - Differential Equations
- Chapter 22 - Algebra of Vectors
- Chapter 23 - Scalar Or Dot Product
- Chapter 24 - Vector or Cross Product
- Chapter 25 - Scalar Triple Product
- Chapter 26 - Direction Cosines and Direction Ratios
- Chapter 27 - Straight Line in Space
- Chapter 28 - The Plane
- Chapter 29 - Linear programming
- Chapter 30- Probability
- Chapter 31 - Mean and Variance of a Random Variable

1. Which is the best guide for the class 12 students to clarify the doubts regarding the Revision Exercise of chapter 18, mathematics?

The RD Sharma Class 12th RE solution material is the best guide for the students to clarify their doubts in the Indefinite Integrals chapter.

2. What are the benefits availed by the students who use RD Sharma books for preparing exams?

They prepare with experts provided solutions.

Numerous practice questions are given.

The material is available for free

3. How many questions are there in the RE of chapter 18, mathematics?

The Revision Exercise (RE) portion consists of 130 questions. You can use the RD Sharma Class 12th RE book for reference.

4. Where can I find the RD Sharma solution books?

The RD Sharma books can be found on the Career 360 website. You can also download any set-off solution materials.

5. Can everyone access the RD Sharma book?

Yes, this solution book is used by students to do their homework, prepare for the exam. The teachers also use it to pick questions for the tests and exams.

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