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


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 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.

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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.

  1. Definition of primitive or antiderivative

  2. Definition and meaning of indefinite integral

  3. Fundamental integration formulae

  4. Some standard results on integration along with the corollary

  5. Integration of trigonometric functions

  6. Integration of exponential functions

  7. Miscellaneous problems

  8. Geometrical interpretation of indefinite integral

  9. Comparison between differentiation and integration

  10.  Methods of integration

  11. Integration by substitution

  12. Some standard results

  13. Evaluation of integrals by using trigonometric substitutions

  14. Some special integrals

  15. Integration by parts

  16. Some important integrals along with theorems

  17. 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

  1. 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. Defined versus Infinite integrals: what's the difference?

An indefinite integral does not have a limit to its integration. Defining a number as a definite integral implies the lower and upper limits are constant. Indefinite integrals represent the derivatives of a family of functions. Every function is different from every other function in the family.

2. When is the integral symbol used?

It is possible to find indefinite integrals by simply omitting the limits of integration from the integral key, which is used to find definite integrals.

3. How does Sigma Notation work?

Sigma notation is sometimes used to compactly represent the sum of similar terms. It is a Greek upper-case letter ​∑ that means "add up all of the following."

Riemann sums can be written with the Sigma notation \displaystyle \sum_{i=1}^{n} (f(x_i)\Delta x)​i=1​∑​n​​(f(xi​​)Δx).

It can be read aloud as "the sum from i equals 1 to n of f of x sub i delta x."

4. What is the procedure for finding the indefinite integral?

A process of finding the indefinite integral of a function is also known as integration or integrating f(x). It can be expressed as follows:

∫f(x)dx = F(x) + C, where C is any real number.

For the antiderivative of a function, we generally use appropriate formulas.

Hence, an indefinite integral yields a function.

5. Indefinite integrals represent what?

An indefinite integral corresponds to a family of functions whose derivatives are f. In the process of integration, only indefinite integrals contain a real number C.