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# RD Sharma Class 12 Solutions Chapter 19 - Indefinite Integrals (Ex 19.12) Exercise 19.12 LIVE
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## RD Sharma Class 12 Solutions Chapter 19 - Indefinite Integrals (Ex 19.12) Exercise 19.12 - Free PDF

Free PDF download of RD Sharma Class 12 Solutions Chapter 19 - Indefinite Integrals Exercise 19.12 solved by Expert Mathematics Teachers on Vedantu.com. All Chapter 19 - Indefinite Integrals Ex 19.12 Questions with Solutions for RD Sharma Class 12 Maths to help you to revise the complete Syllabus and Score More marks. Register for online coaching for IIT JEE (Mains & Advanced) and other engineering entrance exams.

Class 12 Maths is quite important from a lot of aspects. The chapters taught here will be used in both science and commerce as part of higher studies. Engineering aspirants will also have to sit for the Joint Entrance Examination (JEE), where an entire section will be dedicated to just mathematics. The textbook by RD Sharma is quite reputed and is followed by most Class 12 students belonging to the CBSE Board.

Last updated date: 02nd Oct 2023
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## RD Sharma Class 12 Solutions for Maths Book

There are 33 chapters in total in the Class 12 RD Sharma Maths book. None of these chapters can be skipped if you wish to fare well in your Maths exams. Refer to these NCERT Solutions to know more. They have been categorised by exercise number and chapter.

RD Sharma Solutions for  Unit 1 - Relations

RD Sharma Solutions for  Unit 2 - Functions

RD Sharma Solutions for  Unit 3 - Binary Operations

RD Sharma Solutions for  Unit 4 - Inverse Trigonometric Functions

RD Sharma Solutions for  Unit 5 - Algebra of Matrices

RD Sharma Solutions for  Unit 6 - Determinants

RD Sharma Solutions for  Unit 7 - Adjoint and Inverse of a Matrix

RD Sharma Solutions for  Unit 8 - Solution of Simultaneous Linear Equations

RD Sharma Solutions for  Unit 9 - Continuity

RD Sharma Solutions for  Unit 10 - Differentiability

RD Sharma Solutions for  Unit 11 - Differentiation

RD Sharma Solutions for  Unit 12 - Higher-Order Derivatives

RD Sharma Solutions for  Unit 13 - Derivative as a Rate Measurer

RD Sharma Solutions for  Unit 14 - Differentials, Errors and Approximations

RD Sharma Solutions for  Unit 15 - Mean Value Theorems

RD Sharma Solutions for  Unit 16 - Tangents and Normals

RD Sharma Solutions for  Unit 17 - Increasing and Decreasing Functions

RD Sharma Solutions for  Unit 18 - Maxima and Minima

RD Sharma Solutions for  Unit 19 - Indefinite Integrals

RD Sharma Solutions for  Unit 20 - Definite Integrals

RD Sharma Solutions for  Unit 21 - Areas of Bounded Regions

RD Sharma Solutions for  Unit 22 - Differential Equations

RD Sharma Solutions for  Unit 23 - Algebra of Vectors

RD Sharma Solutions for  Unit 24 - Scalar Or Dot Product

RD Sharma Solutions for  Unit 25 - Vector or Cross Product

RD Sharma Solutions for  Unit 26 - Scalar Triple Product

RD Sharma Solutions for  Unit 27 - Direction Cosines and Direction Ratios

RD Sharma Solutions for  Unit 28 - Straight Line in Space

RD Sharma Solutions for  Unit 29 - The Plane

RD Sharma Solutions for  Unit 30 - Linear programming

RD Sharma Solutions for  Unit 31 - Probability

RD Sharma Solutions for  Unit 32 - Mean and Variance of a Random Variable

RD Sharma Solutions for  Unit 33 - Binomial Distribution

## FAQs on RD Sharma Class 12 Solutions Chapter 19 - Indefinite Integrals (Ex 19.12) Exercise 19.12

1. Why is Class 12 Maths important?

Knowing Maths is a requirement for many degrees in India. Class 12 Maths introduces topics and concepts that will prove useful to students in the coming years. To build a strong base in the future, students need to have a good understanding of this subject from their formative years. Moreover, Maths seems daunting simply because the syllabus of the subject is huge. Once you start going through the theory portion of each chapter and get to solving exercises, you will find that most of the sums are quite easy.

2. Why do students prefer the RD Sharma Maths textbook in Class 12?

Mr RD Sharma is a renowned teacher who aims to make Maths simple and comprehensive for everyone. His books present information in an easy-to-understand manner that does not overwhelm young students. After a new concept is introduced, solved examples are given to help demonstrate how a sum should ideally be solved. The book is a great resource for all Maths lovers and is recommended by experts worldwide. The solutions are also organised chapter-wise and are further categorised into various exercises.

3. What is Chapter 31 of RD Sharma’s textbook all about?

Chapter 31 of RD Sharma’s Class 12 Maths textbook is on Probability. Probability is a very useful tool that is part of mathematical reasoning and modelling. A lot of statistics are based on data compiled using probability. In other words, to put it simply, the probability is a number that reflects the chance or likelihood of a particular event occurring. Probabilities can be expressed as proportions and percentages. In the case of proportions, they can range from 0 to 1 while in the case of percentages, they can be seen ranging from 0% to 100%.

4. What are the various applications of integration?

Integration is used by scientists and engineers alike. It is part of computational analysis. Integration is mainly of 2 types: definite and indefinite. In Chapter 19 of the Class 12 RD Sharma Maths textbook, students are made to deal with Indefinite Integrals. We know definite integrals can be used to find the area under a curve. Similarly, they can also be used to find the area between two curves. To do so efficiently, find the area between two curves defined by functions and then try to integrate the difference of the functions. In contrast to this, an indefinite integral is a function that takes the antiderivative of another function.

5. How are NCERT Solutions helpful for solving sums on Indefinite Integrals?

Vedantu’s NCERT Solutions are the most reliable academic resource available for students in Class 12. With board exams looming around the corner, students are anxious and unable to figure out which chapters to complete first in Maths as the syllabus is huge. NCERT Solutions help pinpoint the important areas of the entire syllabus. Questions are asked on topics that come frequently in school and competitive exams alike. Students are made thorough in their concepts and the importance of regular practice in Maths is highlighted.