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Edited By Kuldeep Maurya | Updated on Jan 24, 2022 02:22 PM IST

The class 12 students require a proper guide other than their teachers and tutors to help them clarify their doubts. The RD Sharma books are one of the best solution materials recommended by many CBSE schools to their students. However, most of the Class 12 students find it challenging to solve the mathematics, chapter 19 sums. In such cases, the RD Sharma Class 12th Exercise 19.3 is essential.

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Download E-bookDefinite Integrals Exercise 19.3 Question 1(i)

Now break the limit =

Definite Integrals Exercise 19.3 Question 1(ii)

Definite Integrals Exercise 19.3 Question 1(iii)

Definite Integrals Exercise 19.3 Question 1(iv)

Definite Integrals Excercise 19.3 Question 3

Definite Integrals Excercise 19.3 Question 4

Using the formula:

Definite Integrals Excercise 19.3 Question 5

Use the formula:

Definite Integrals Exercise 19.3 Question 6

Also we know that:

Definite Integrals Exercise 19.3 Question 8

Definite Integrals Exercise 19.3 Question 9

Definite Integrals Exercise 19.3 question 10

Definite Integrals Exercise 19.3 question 11

We know that

Definite Integrals Exercise 19.3 question 12

Definite Integrals Exercise 19.3 question 13

Definite Integrals Exercise 19.3 Question 15

Definite Integrals Exercise 19.3 Question 16

Definite Integrals Exercise 19.3 Question 17

We know that,

Definite Integrals Excercise 19.3 Question 18

For the first integrand:

For the second integrand:

For the third integrand:

Hence the total integration will be

Definite Integrals Excercise 19.3 Question 19

We know that,

Definite Integrals Excercise 19.3 Question 20

Definite Integrals Excercise 19.3 Question 21

Consider

Now

Definite Integrals Excercise 19.3 Question 22

We will use the formula

So,

Definite Integrals Excercise 19.3 Question 23

… (i)

Consider,

Now, use the property:

… (ii)

Adding (i) and (ii) , we get

Definite Integrals Exercise 19.3 Question 24

This shows that f(x) is an even function.

So we use the property :

Definite Integrals Exercise 19.3 Question 25

`

Definite Integrals Exercise 19.3 Question 26

Let

Put and differentiate on both sides

Now by partial fraction

Equating coefficients of both sides

[any validated up with becomes ]

Definite Integrals Exercise 19.3 question 27

Definite Integrals Exercise 19.3 question 28

**Answer:****Hint:** You must know about the rules of solving definite integral.**Given:****Solution:**

Class 12, Mathematics, chapter 19, Definite Integrals, is a part where the students take a lot of time to understand the complex concepts. The third exercise, ex 19.3, consists of 31 questions, including its subparts to be solved by the students. These questions are divided into levels 1 and 2 according to their difficulty standards. Students can find solutions for all these questions in a single RD Sharma Class 12 Chapter 19 Exercise 19.3 book whenever they have doubts.

A group of staff members who are experts in their respective domains has created solutions for these questions. They have provided solutions in every way possible for a single sum. As it follows the NCERT patterns, CBSE school students can use the RD Sharma books to clarify their doubts. This RD Sharma Class 12th Exercise 19.13 solution book also consists of various practice questions that help the students work out and gain confidence to face the challenging questions in the exams.

Definite Integrals would no more be a complex concept once practiced well. The students can use this resource material, Class 12 RD Sharma Chapter 19 Exercise 19.3 Solution, to do their homework and assignment. They can also use it to prepare for their tests and examinations. With a copy of RD Sharma Class 12th Exercise 19.3 solution book, the students need not have a teacher or tutor by their side always. RD Sharma's book offers excellent guidance in solving students' doubts.

The most significant advantage of using RD Sharma books is that they can be accessed for free of cost at the Career360 website. The option to download the RD Sharma Class 12th Exercise 19.3 material is also available. Lots of students have already benefitted by scoring high marks using RD Sharma books for their exam preparation.

There are chances that questions for the public exams will be picked from the RD Sharma books. Hence, for the students preparing for their exams, using the RD Sharma Class 12 Solutions Chapter 19 Ex 19.3 book from day one will help them score better.

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. Why is RD Sharma Books used by most of the Class 12 students who are preparing for the public examinations?

Firstly, the solutions provided in these books are given by the experts, verified to be accurate. Secondly, there were instances when practicing questions from the RD Sharma Class 12th Exercise 19.3 portion being asked for the public exam. Hence, many students use these books.

2. Is it possible to find the RD Sharma solution books for free of cost?

Visit the Career 360 website to access the best set of RD Sharma solution books for free of cost. You need not make any payment to access these books.

3. Can the RD Sharma solution books be downloaded?

The RD Sharma Class 12 Solutions Definite Integrals Ex 19.3 book can be download to your device. You need to hit the Download button present on the screen near the book you require.

4. How can I view the RD Sharma solution book for the class 12 chapter 19, ex 19.3 portions?

Visit the Career 360 website and type the name of the book in the Search box. The results will be displayed accordingly. In this case, type RD Sharma Class 12th Exercise 19.3 solution book to find the answer key accordingly.

5. Can CBSE board students refer to the RD Sharma solution books to clear their doubts?

The RD Sharma solution books follow the NCERT pattern; hence the CBSE board students can very well refer to these books to clarify their doubts.

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