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Edited By Kuldeep Maurya | Updated on Jan 24, 2022 09:27 AM IST

Class 12 RD Sharma chapter 18 exercise 18.25 solution provides the best material for maths for CBSE students. It has been highly recommended by students, teachers as well as experts for the thorough practice to perform well in the board exams. The RD Sharma class 12th exercise 18.25 will give you the best solution so that you will not find any need to refer to any resource for help while solving maths.

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Chapter 18 - Indefinite Integrals - Ex-18.1

Indefinite Integrals Exercise 18.25 Question 1

We have,

Indefinite Integrals Exercise 18.25 Question 2

We know that,

Indefinite Integrals Exercise 18.25 Question 3

We have,

Indefinite Integrals Exercise 18.25 Question 4

We have,

Indefinite Integrals Exercise 18.25 Question 5

We Know that,

Indefinite Integrals Exercise 18.25 Question 6

Indefinite Integrals Exercise 18.25 Question 7

By integrating w.r.t x

So we get,

Now apply by parts method

On further simplification,

Indefinite Integrals Exercise 18.25 Question 8

Integrate on by parts applying once again

Indefinite Integrals Exercise 18.25 Question 9

We can integrate by parts in this way

Indefinite Integrals Exercise 18.25 Question 10

Then,

Consider the 1st function as log t and 2nd function

Let

By integrating w.r.t ‘t’

Again by integrating the second term we get

Replacing t with logx

By taking log x as common

Indefinite Integrals Exercise 18.25 Question 11

Now apply by part method again

On further simplification,

Indefinite Integrals Exercise 18.25 Question 12

Indefinite Integrals Exercise 18.25 Question 13

Evaluate the integral part by part

Integration by parts

Let

Now

Combining all,

Indefinite Integrals Exercise 18.25 Question 15

Again by integrating the second part

So we get

Indefinite Integrals Exercise 18.25 Question 16

Now by integrating the second part we have,

Indefinite Integrals Exercise 18.25 Question 17

By integrating w.r.t ‘t’ taking the first function as t and second function as

Now by replacing t with

By taking as common

Indefinite Integrals Exercise 18.25 Question 18

We can write it as

Now by integrating the second part

Substituting the value of t as

Indefinite Integrals Exercise 18.25 Question 19

Sin 2x = 2 sinxcosx, it can be written as and consider first

function as x and second function as sin2x

Again by integrating second term

By further simplification,

Indefinite Integrals Exercise 18.25 Question 20

So we get,

Again by integrating the second term

Indefinite Integrals Exercise 18.25 Question 21

Again integrating by parts, we obtain

Indefinite Integrals Exercise 18.25 Question 22

[Now integrate by parts]

Indefinite Integrals Exercise 18.25 Question 24

Indefinite Integrals Exercise 18.25 Question 26

Indefinite Integrals Exercise 18.25 Question 27

[Using integration by parts]

Indefinite Integrals Exercise 18.25 Question 28

Let

Indefinite Integrals Exercise 18.25 Question 29

Substituting the value of t in equation (1)

Indefinite Integrals Exercise 18.25 Question 30

Assume that

Differentiating w.r.t to ‘t’

.................(iii)

Now substituting values from equation (ii) & equation (iii)

Here, use integration Identity

...........(iv)

Assume

...........(v)

Differentiate w.r.t ‘y’

............(vi)

Substituting values from equation (v) and equation (vi) in integral of equation (iv)

Use integration identity

Substitute the value of y from equation (v)

Substitute the value of ‘t’ from equation (ii)

So,

Indefinite Integrals Exercise 18.25 Question 35

Indefinite Integrals Exercise 18.25 Question 38

Indefinite Integrals Exercise 18.25 Question 51

Integrate by parts, taking as the first function

Indefinite Integrals Exercise 18.25 Question 52

Applying by parts

Indefinite Integrals Exercise 18.25 Question 54

Applying by parts,

Indefinite Integrals Exercise 18.25 Question 55

Take the first function as x and second function as sinx and sin 3x

Indefinite Integrals Exercise 18.25 Question 58

Applying by parts

RD Sharma class 12th exercise 18.25 contains 61 questions from the RD Sharma class 12 solution of Indefinite integrals exercise 18.25 that are presented in the most basic format and hence the concepts covered are -

Applications of integration

Applications of indefinite integration

Area under a curve by integration

Centroid of area by integration

Some integrals theorems

The RD Sharma class 12 solution chapter 18 exercise 18.25 consists of a lot of questions that give a brief understanding of the chapter.

The solutions of the RD Sharma class 12th exercise 18.25 are designed by experts of maths and give you extraordinary questions to tighten your maths skills.

The solutions also provide helpful tips and solved questions for better reference and understanding maths in an easy way.

Teachers use the solution of RD Sharma class 12 chapter 18 exercise 18.25 for preparing lectures and giving homeworks.

The RD Sharma class 12th exercise 18.25 can be downloaded from Careers360 website for online PDFs and study materials for free of cost.

The solutions are trusted by every student, teacher, and schools as well for nurturing the students with the authentic knowledge of mathematics.

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Download E-book**RD Sharma Chapter-wise Solutions**

- 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. What is the use of this study material?

Students appearing for the 12th board exams can refer to these solutions for practicing maths

2. Can I score high marks after practicing from the RD Sharma solutions?

Yes, a thorough practice of the RD Sharma solution can help you ace the subject of maths and score real high marks in board exams.

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