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# RD Sharma Class 12 Solutions Chapter 19 - Indefinite Integrals (Ex 19.14) Exercise 19.14

Last updated date: 08th Aug 2024
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## RD Sharma Class 12 Solutions Chapter 19 - Indefinite Integrals (Ex 19.14) Exercise 19.14 - Free PDF

Free PDF download of RD Sharma Class 12 Solutions Chapter 19 - Indefinite Integrals Exercise 19.14 solved by Expert Mathematics Teachers on Vedantu. All Chapter 19 - Indefinite Integrals Ex 19.14 Questions with Solutions for RD Sharma Class 12 Maths help you to revise the complete Syllabus and score more marks.

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All of the information for CBSE RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.14 has been provided. Any questions or concerns should be posted in the comments area.

RD Sharma Solutions for Class 12 Maths Exercise 19.14 Chapter 19 – This page contains information about indefinite integrals. The exercise includes several unique integrals as well as proof. The given integrals should be solved using these results. RD Sharma Solutions for Class 12 are required reading for students who are having difficulty understanding and solving questions.

These solutions were developed by Vedantu experts who took into account the students' conceptual understanding to meet their needs. Students will benefit from the detailed solutions in achieving good grades on the topic. Here you will find the PDF of RD Sharma Solutions for Class 12 Maths Chapter 19 Exercise 19.14. Students can use the links provided below to refer to and download information.

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## RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.14

Students can use the PDF as a reference guide to help them understand and practice to do well on the Class 12 exam. Working with RD Sharma Solutions regularly helps students enhance their problem-solving and logical thinking skills. This is essential for improving academic results.

### Chapter 19 Exercise 19.14: Important Topics from the Chapter RD Sharma Solutions Class 12 Maths

• The following are some of the key themes discussed in RD Sharma Solutions Class 12 Maths Chapter 19 – Indefinite Integrals Exercise 19.14.

• The term antiderivative is defined as Indefinite integral.

• Formulas for basic integration

• Some standard integration findings, as well as the corollary

• Trigonometric functions integration

• Exponential functions' integration

• Problems of many kinds

• Indefinite integral's geometric interpretation

• Differences and similarities between differentiation and integration

• Integration techniques

• Substitutional integration

• Some typical outcomes

• Using trigonometric substitutions to evaluate integrals

• Some unique integrals

• Parts-based integration

• Some key integrals, as well as theorems

• Using partial fractions to integrate rational algebraic functions

• When the denominator can be expressed as a product of linear components

• When there are some repeated linear components in the denominator

• There are irreducible quadratic factors in the denominator.

### Ex 19.14 Example 1: Indefinite Integrals

Let     I = $\int \frac{1}{a^{2}-b^{2}x^{2}}dx$

= $\frac{1}{b^{2} }\int\frac{1}{\frac{a^{2}}{b^{2}}-x^{2}}dx$

= $\frac{1}{b^{2}}\int \frac{1}{(\frac{a}{b})^{2}-x^{2}}dx$

I =$\frac{1}{b^{2} }\times \frac{1}{2\times (\frac{a}{b})}log\left | \frac{\frac{a}{b}+x}{\frac{a}{b}-x} \right |+c$ ($since\int \frac{1}{a^{2}-x^{2}}dx=\frac{1}{2a}log\left | \frac{x+a}{x-a} \right |+c$)

I = $\frac{1}{2ab}log\left | \frac{a+bx}{a-bx} \right |+c$

Hence the article provides important information such as the Important Topics from the Chapter RD Sharma Solutions Class 12 Maths. Students should visit the website of Vedantu and practice questions.

## FAQs on RD Sharma Class 12 Solutions Chapter 19 - Indefinite Integrals (Ex 19.14) Exercise 19.14

1. Is the RD Sharma Class 12 Solutions Chapter 19 – Indefinite Integrals PDF useful?

The RD Sharma Class 12 Solutions Chapter 19 – Indefinite Integrals PDF is very useful. It has extensive and comprehensive problem solutions that can help students to attain good marks in their 12th board examination. Students need to carefully read and learn the mathematical problems and solve them on their own. The solutions provided in the free PDF are simple to read and easy; this will help them correct their answers and learn from their mistakes. One needs to practise daily to get the full benefit out of the RD Sharma Class 12 Solutions Chapter 19 – Indefinite Integrals (Ex 19.14) Exercise 19.14 – Free PDF.

2. How to study for the 12th board examinations with RD Sharma Class 12 Solutions Chapter 19 – Indefinite Integrals (Ex 19.14) Exercise 19.14 – Free PDF?

Students should dedicate a few hours to study for their 12th board examinations. You are required to study extra due to the tough subjects like mathematics, physics, chemistry, and biology. The commerce and art students should also devote at least two hours daily to study their books. Students should take online coaching classes to score well in the 12th board examinations. The RD Sharma Class 12 Solutions Chapter 19 – Indefinite Integrals (Ex 19.14) Exercise 19.14 – Free PDF can help students who have mathematics. Register for online classes by Vedantu now.

3.  Is RD Sharma enough for 12th board preparations?

Students should study their syllabus NCERT book thoroughly for their 12th board examinations. These examinations take place at the national level and focus on NCERT. If you are thorough with the syllabus of the NCERT mathematics book, you should opt for RD Sharma for advanced studies. Vedantu offers easy to learn and step by step explanations of simple to the most difficult mathematical problems in the form of free PDF.