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Quick Solution for RD Sharma Class 12 Chapter 19 Exercise 19.27

Last updated date: 17th May 2024
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RD Sharma Class 12 Solutions Chapter 19 - Indefinite Integrals (Ex 19.27) Exercise 19.27 - Free PDF

Studying RD Sharma Class 12 Chapter 19 has never been easier. You can now download and use the solutions of the exercises of Indefinite integrals from here and learn the concepts clearly. Develop your conceptual foundation by choosing this solution file and learn how to approach such questions efficiently.

Free PDF download of RD Sharma Class 12 Solutions Chapter 19 - Indefinite Integrals Exercise 19.27 solved by expert mathematics teachers of Vedantu. All Chapter 19 - Indefinite Integrals Ex 19.27 Questions with Solutions for RD Sharma Class 12 Maths are designed to help you to revise the complete Syllabus and Score More marks. 

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Competitive Exams after 12th Science

An Introduction to Indefinite Integrals

The indefinite integral is known as the integration of a function without any particular limits. Integration is just the reverse process of differentiation and it is referred to as the antiderivative of the given function. The indefinite integral is a very important part of the calculus for class 12 students in their exams and the application of limiting points to the integral transforms it into definite integrals. Integration is defined for a function, say f(x) and it helps in finding the area enclosed by the curve when it is represented on a graph with reference to one of the coordinate axes.

What is an Indefinite Integral? 

The indefinite integral is known as the integration of a function without any particular limits. Integration is just the reverse process of differentiation and it is referred to as the antiderivative of the given function. For a function, say f(x), if the derivative is represented by f'(x), the integration of the resultant of(x) gives us back the initially given function f(x).


Applications of Indefinite Integration

Indefinite integral has many numerous applications in calculus. The concept of indefinite integration can be used to find the area enclosed by the equation of the given curve. Further, on applying limits, the given indefinite integral gets transformed into a definite integral, which helps in the calculation of the area enclosed by this particular curve.

Download this solution file for this chapter and study the exercise well. Understand how the problems of this exercise are approached by the experts of Vedantu by following the standard CBSE guidelines. Save your time by learning the best methods and ap[plying them to solve problems in the upcoming exams. 

FAQs on Quick Solution for RD Sharma Class 12 Chapter 19 Exercise 19.27

1. What are some of the methods that can be used to solve indefinite integrals? 

Indefinite Integrals can be solved by many different approaches but some of the most efficient methods are as follows:

  • Integration by parts method

  • Integration by substitution method

  • Integration by partial fractions method

  • Integration by inverse trigonometric functions method

2. How can we use integration by parts method?

The integration by parts method is the integration of the product of two of the given functions. In mathematics, the two functions are generally represented by f(x) and g(x). Amongst the two functions, the first function f(x) is selected so that its derivative formula exists, and the second function g(x) is chosen so that an integral of such a function seems to exist.

∫ f(x).g(x).dx = f(x) ∫ g(x).dx - ∫(f'(x) ∫g(x).dx).dx + C 

This formula for integration by parts method can be applied for functions or expressions in which the derivatives do not exist, and which cannot be integrated by any simple process of the integration. Here, we try to use the formula of integration by parts method and try to find the integral of the product of the two or more functions. This formula can be applied for the logarithmic functions and for the inverse trigonometric functions which cannot be integrated using any of the simple processes of simple integration.

3. How can we use integration by substitution method?

Integration by substitution method is an important method in the topic of integration, which is used when a function to be integrated is either a complex function or if the direct integration of the function is not completely feasible. The process of integration by substitution method is used if the given function is to be integrated as one of the following three characteristics.

  • The given function has a particular sub-function.

  • The function to be integrated is a complex numerical-based function.

  • The direct integration of the given function is not quite possible.

4. How can we use integration by partial fractions method?

Integration by partial fractions method is a method used to kind of decompose and then further integrate a rational fraction integrand that has complex terms in its denominator. By using the partial fraction method, we can calculate and decompose the expression into simpler and smaller terms so that we can easily calculate or integrate the expression thus obtained from before. Some of the major applications of integration by partial fractions method include Integrating rational fraction in Calculus, finding the Inverse Laplace Transform in the theory of differential equations and it is mostly used to decompose the fraction into any two or more different fractions. 

5. What is the Difference Between Indefinite Integrals and Definite Integrals?

If we focus on the solutions provided in the PDF file of Vedantu, you can easily find the difference between indefinite integrals and definite integrals in the application of the limiting points. In Indefinite integrals, we apply the lower limit and the upper limit to the points, and in indefinite integrals are computed for the entire range without any of the limits.

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