RD Sharma Class 12 Solutions Chapter 19 - Indefinite Integrals (Ex 19.10) Exercise 19.10

Q: 3. Why is it essential to add the constant of integration '+ C' in every solution for this chapter?

The indefinite integral of a function represents a whole family of functions whose derivatives are the same. The constant 'C' accounts for all these possible functions. Forgetting to add '+ C' in your final answer is a common mistake and can lead to a loss of marks in exams, as it represents an incomplete solution.

RD Sharma Class 12 Solutions Chapter 19 - Indefinite Integrals (Ex 19.10) Exercise 19.10 - Free PDF

Free PDF download of RD Sharma Class 12 Solutions Chapter 19 - Indefinite Integrals Exercise 19.10 solved by Expert Mathematics Teachers on Vedantu.com. All Chapter 19 - Indefinite Integrals Ex 19.10 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.

Here is a set of RD Sharma Class 12 Solutions for Chapter 19 - Indefinite Integrals.

The RD Sharma Solutions for Class 12 students will help students develop better skills and prepare efficiently for exams. We offer RD Sharma solutions with conceptual problems and examples to help students understand the concept better. Mathematicians are advised to study differential equations as one of the most relevant topics to study. Students need to master the material. In addition to the solutions, our subject matter experts have designed the Chapter 19 problems in a way that will make solving them fun. RD Sharma Class 12 solutions are available online on the website for free, and students can access them by clicking the links provided below.

The indefinite integral of a function f is a differentiable function F whose derivative is equal to the original function f. In another way, we can say f is the derivative of F (F' = f). For Class 12 Maths, RD Sharma Solutions is going to explain how to find indefinite integrals using different methods. These methods include substitution, parts method, and partial fraction method. In the examination, this chapter is very heavily weighted. RD Sharma Class 12 Solutions Indefinite Integrals are designed so that the students can learn the concepts quickly and easily.

Indefinite Integrals:

The indefinite integral is the opposite of the derivative. In other words, it is an antiderivative of a function. Indefinite integrals can be solved by adding a constant term to the integral of x to the nth power. Calculating this integral takes one divided by n+1 times x to the n+1 power.

Indefinite integrals are functions that take the antiderivative of a function. In terms of visual representation, it is a function, a symbol, and finally a symbol. A simple way to symbolize the antiderivative is through the indefinite integral symbol. While indefinite and definite integrals are related, they are not the same.

The RD Sharma Class 12 Mathematics Solutions Chapter 19 The Indefinite Integral

Following is a list of a few of the most important topics in this chapter.

Definition of primitive or antiderivative
Definition and meaning of indefinite integral
Fundamental integration formulae
Some standard results on integration along with the corollary
Integration of trigonometric functions
Integration of exponential functions
Miscellaneous problems
Geometrical interpretation of indefinite integral
Comparison between differentiation and integration
Methods of integration
Integration by substitution
Some standard results
Evaluation of integrals by using trigonometric substitutions
Some special integrals
Integration by parts
Some important integrals along with theorems
Integration of rational algebraic functions by using partial fractions

17.1 When the denominator is expressible as a product of distinct linear factors

17.2 When the denominator contains some repeating linear factors

17.3 The denominator contains irreducible quadratic factors

Integration of some special irrational algebraic functions

FAQs on RD Sharma Class 12 Solutions Chapter 19 - Indefinite Integrals (Ex 19.10) Exercise 19.10

1. Where can I find reliable, step-by-step solutions for RD Sharma Class 12 Maths Exercise 19.10?

Vedantu provides clear and accurate step-by-step solutions for all problems in RD Sharma Class 12 Maths Chapter 19, Exercise 19.10 on Indefinite Integrals. These solutions are prepared by expert teachers to help you understand the correct method for solving each question.

2. What is the core concept needed to solve the problems in Exercise 19.10 of Indefinite Integrals?

To solve the questions in this exercise, you must be proficient in the method of substitution. This involves identifying a part of the function to substitute with a new variable, which simplifies the integral into a standard form that can be solved easily using basic integration formulas.

3. Why is it essential to add the constant of integration '+ C' in every solution for this chapter?

The indefinite integral of a function represents a whole family of functions whose derivatives are the same. The constant 'C' accounts for all these possible functions. Forgetting to add '+ C' in your final answer is a common mistake and can lead to a loss of marks in exams, as it represents an incomplete solution.

4. How can I best use these RD Sharma solutions to prepare for my board exams?

For effective preparation, you should first attempt to solve the problems yourself. When you are stuck, use Vedantu's solutions to understand the specific step or substitution you missed. Focus on the logic behind the method, not just memorising the steps. This practice builds a strong foundation for tackling similar problems in your exams.

5. Are the methods shown in these solutions valid for the CBSE Class 12 Maths board exam?

Yes, all solutions provided for RD Sharma Class 12 are created by subject matter experts and are fully aligned with the CBSE curriculum and marking guidelines for 2025-26. The step-by-step approach is designed to ensure you write answers that can fetch full marks.

6. How do I know what expression to substitute when solving integrals in this exercise?

A good rule of thumb is to look for a function within the integral whose derivative is also present as a factor. For example, in ∫f(g(x))g'(x)dx, you would substitute u = g(x). With practice, you will learn to quickly spot these patterns in different types of functions covered in RD Sharma.

7. Besides forgetting '+ C', what is another common error students make in indefinite integration?

A frequent error is incorrect algebraic or trigonometric simplification before integration. Students often apply the wrong identity or make a calculation mistake while simplifying the function, which leads to an incorrect integral. Always double-check your simplification before applying an integration formula or method.