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Edited By Kuldeep Maurya | Updated on Jan 24, 2022 02:21 PM IST

RD Sharma class 12th exercise VSA is an extremely important book for all students who are in class 12. RD Sharma solutions is a trusted and famous name among numerous other NCERT solutions. Students and teachers highly recommend this book especially for its Mathematics solutions. The RD Sharma class 12 chapter 19 exercise VSA, especially can be an excellent guidebook for students who want to study and home well before their board exams..

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Definite Integrals exercise Very short answer type question 1

Definite Integrals exercise Very short answer type question 2

Definite Integrals exercise Very short answer type question 3

Definite Integrals exercise Very short answer type question 4**Answer: **

Definite Integrals exercise Very short answer type question 5

We know that

Definite Integrals exercise Very short answer type question 6

Hence, f(x) is an odd function.

Since, if f(x) is an odd

Definite Integrals exercise Very short answer type question 7

Definite Integrals exercise Very short answer type question 8

Definite Integrals exercise Very short answer type question 9

Definite Integrals exercise Very short answer type question 10

Definite Integrals exercise Very short answer type question 11

Use the formula

Definite Integrals exercise Very short answer type question 13

Definite Integrals exercise Very short answer type question 14

..................(ii)

Adding (i) and (ii)

Definite Integrals exercise Very short answer type question 15

Property:

................(ii)

Adding (i) and (ii),

Property:

..................(ii)

Add (i) and (ii)

Definite Integrals exercise Very short answer type question 17

Definite Integrals exercise Very short answer type question 18

Let

Hence, f(x) is an odd function.

Since, if f(x) is an odd.

Definite Integrals exercise Very short answer type question 19

Definite Integrals exercise Very short answer type question 20

Using property

................(ii)

Add (i) and (ii)

Definite Integrals exercise Very short answer type question 21

Definite Integrals exercise Very short answer type question 22

Definite Integrals exercise Very short answer type question 23**Answer: **

Definite Integrals exercise Very short answer type question 24

Definite Integrals exercise Very short answer type question 25

Put

Definite Integrals exercise Very short answer type question 26

Put

Definite Integrals exercise Very short answer type question 27

Definite Integrals exercise Very short answer type question 28

Definite Integrals exercise Very short answer type question 29

Definite Integrals exercise Very short answer type question 30

Definite Integrals exercise Very short answer type question 31

Definite Integrals exercise Very short answer type question 32

Definite Integrals exercise Very short answer type question 33

Definite Integrals exercise Very short answer type question 34

Definite Integrals exercise Very short answer type question 35

Integrating both sides

Definite Integrals exercise Very short answer type question 36

Let ..............(i)

Taking logarithm on both sides

........(ii)

From eqn (i) and (ii) we can write

This means instead of integrating we will integrate

Definite Integrals exercise Very short answer type question 37

Definite Integrals exercise Very short answer type question 38

Definite Integrals exercise Very short answer type question 39

Definite Integrals exercise Very short answer type question 40

Integration of exponential function is same as the function

Definite Integrals exercise Very short answer type question 41**Answer: **

Definite Integrals exercise Very short answer type question 42

We know the values of greatest integer function on

Definite Integrals exercise Very short answer type question 43

Using rule of greatest integer

Definite Integrals exercise Very short answer type question 44

And when

[ using the value of greatest integer function ]

Note: Final answer is not matching with the book.

Definite Integrals exercise Very short answer type question 45

The RD Sharma class 12 solutions Definite Integrals VSA can be an excellent free study material for students who will appear for their board exams. Chapter 19 of the NCERT maths book deals with Definite Integral, Evaluating Definite Integrals, Definite Integral & Riemann integral Formulas, etc. Exercise VSA has 45 questions that require short and simple answers. The RD Sharma class 12th exercise VSA will guide you while you attempt to solve these questions.

The class 12 RD Sharma chapter 19 exercise VSA solution is a lucrative book of answers that will do wonders when practiced thoroughly. Students who have used the RD Sharma class 12 solutions Definite Integrals ex VSA in the past have found common questions in their board exams. Professionals in mathematics and teachers in India are responsible for drafting the RD Sharma class 12 solutions chapter 19 ex VSA book. Therefore, they contain some unique and improved methods of calculations rarely taught in class.

The RD Sharma class 12th exercise VSA always comes with the latest syllabus as it is updated with every new edition of the NCERT books. Students will find all answers to their NCERT questions in this book. Homework questions can also be answered with the help of this book, as teachers like to give questions from RD Sharma class 12th exercise VSA to test their student's progress.

Students can make use of these solutions to mark their performance and improve their weak areas so that they can solve all math problems without making any mistakes. The free copy of the RD Sharma class 12th exercise VSA pdf can be easily downloaded from the Career360 website, which is the one-stop destination for all RD Sharma 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. Is the latest version of class 12 RD Sharma chapter 4 exercise 4.5 solution book available online?

The class 12 RD Sharma chapter 19 exercise VSA solution book is always available, and the pdfs are updated regularly with any change in the CBSE syllabus. All answers provided in RD Sharma Solutions will correspond to the NCERT questions in the textbook.

2. In what ways does the RD Sharma class 12th exercise VSA help the students in completing their challenging homework?

Most of the homework questions given for the students are asked from the RD Sharma Class 12th exercise VSA solutions book. When the students own a copy of the RD Sharma Class 12th exercise VSA book, they can complete their homework effortlessly.

3. How can RD Sharma class 12 solutions Definite Integrals ex VSA be helpful for me?

The RD Sharma class 12 solutions Definite Integrals ex VSA can be a guide for students as it can help them test themselves on their recent lessons. They can use the answers in the book to check their own answers and see if they have made any mistakes.

4. Is the RD Sharma Class 12 Solutions Chapter 19 ex VSA used only by the students?

The RD Sharma Class 12 Solutions Chapter 19 Ex VSA reference guides are used by the students to clarify their doubts in the homework. Most of the teachers and mathematics tutors also refer to this guide to get ideas of solving sums quickly.

5. Where is the soft copy for the RD Sharma Class 12th exercise VSA available?

The students need not depend on hardcover solution books these days. The RD Sharma Class 12th Exercise VSA books can be downloaded from the Career 360 website and viewed from a laptop or smartphone according to their convenience.

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