UPSC Exam > UPSC Notes > Mathematics Optional Notes for UPSC > Indefinite Integrals
Indefinite Integrals | Mathematics Optional Notes for UPSC PDF Download
| Download, print and study this document offline |
Please wait while the PDF view is loading
Page 1
Edurev123
4. Indefinite Integrals
4.1 Does the integral ?
-?? ?? ?v
?? +?? ?? -?? ???? exist? If so, find its value.
(2010 : 12 Marks)
Solution:
Given the integral is ?
-1
1
?v
1+?? 1-?? ????
Rationalizing integrand, we get
? ?
1
-1
?
v(1+?? )
2
v1-?? 2
???? =? ?
1
-1
?
1+?? v1-?? 2
????
Let ?? -sin?? ,? ???? =cos ?????? ? Integral becomes ? ?
?? -?? ?
1+sin ?? v1-sin
2
?? ???? ×cos ?? =? ?
?? /2
-?? /2
?
1+sin ?? |cos ?? |
×cos ?????? =? ?
?? /2
-?? /2
?(1+sin ?? )????
=[?? ]
-?? /2
?? /2
+0=??
Read More
|
387 videos|203 docs
|
FAQs on Indefinite Integrals - Mathematics Optional Notes for UPSC
| 1. What is an indefinite integral in UPSC mathematics? |  |
Ans. An indefinite integral in UPSC mathematics is the reverse process of differentiation. It involves finding a function that, when differentiated, gives the original function.
| 2. How is the symbol for indefinite integral represented in UPSC mathematics? | |
Ans. The symbol for indefinite integral in UPSC mathematics is ∫ (integral symbol), followed by the function to be integrated and dx to represent the variable of integration.
| 3. What is the significance of finding indefinite integrals in UPSC mathematics? | |
Ans. Finding indefinite integrals in UPSC mathematics helps in solving problems related to areas under curves, velocity, distance, and various other physical and mathematical concepts.
| 4. Can indefinite integrals have multiple solutions in UPSC mathematics? | |
Ans. Yes, indefinite integrals can have multiple solutions in UPSC mathematics due to the presence of arbitrary constants that arise during the integration process.
| 5. How can one evaluate indefinite integrals efficiently in UPSC mathematics? | |
Ans. One can evaluate indefinite integrals efficiently in UPSC mathematics by using integration techniques such as substitution, integration by parts, trigonometric integrals, and partial fractions.
Related Exams
About this Document
|
4.70/5 Rating |
|
Oct 31, 2024 Last updated |
Document Description: Indefinite Integrals for UPSC 2024 is part of Mathematics Optional Notes for UPSC preparation.
The notes and questions for Indefinite Integrals have been prepared according to the UPSC exam syllabus. Information about Indefinite Integrals covers topics
like and Indefinite Integrals Example, for UPSC 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Indefinite Integrals.
Introduction of Indefinite Integrals in English is available as part of our Mathematics Optional Notes for UPSC
for UPSC & Indefinite Integrals in Hindi for Mathematics Optional Notes for UPSC course.
Download more important topics related with notes, lectures and mock test series for UPSC
Exam by signing up for free. UPSC: Indefinite Integrals | Mathematics Optional Notes for UPSC
Description
Full syllabus notes, lecture & questions for Indefinite Integrals | Mathematics Optional Notes for UPSC - UPSC | Plus excerises question with solution to help you revise complete syllabus for Mathematics Optional Notes for UPSC | Best notes, free PDF download
Information about Indefinite Integrals
In this doc you can find the meaning of Indefinite Integrals defined & explained in the simplest way possible. Besides explaining types of
Indefinite Integrals theory, EduRev gives you an ample number of questions to practice Indefinite Integrals tests, examples and also practice UPSC
tests
|
Explore Courses for UPSC exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
Related Searches
Semester Notes
,Indefinite Integrals | Mathematics Optional Notes for UPSC
,Free
,Indefinite Integrals | Mathematics Optional Notes for UPSC
,past year papers
,Previous Year Questions with Solutions
,Sample Paper
,Viva Questions
,MCQs
,shortcuts and tricks
,practice quizzes
,Exam
,mock tests for examination
,Important questions
,Objective type Questions
,Summary
,study material
,ppt
,Extra Questions
,video lectures
,Indefinite Integrals | Mathematics Optional Notes for UPSC
;
Additional Information about Indefinite Integrals for UPSC Preparation
Indefinite Integrals Free PDF Download
The Indefinite Integrals is an invaluable resource that delves deep into the core of the UPSC exam.
These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective.
With the help of these notes, you can grasp complex subjects quickly, revise important points easily,
and reinforce your understanding of key concepts. The study notes are presented in a concise and easy-to-understand manner,
allowing you to optimize your learning process. Whether you're looking for best-recommended books, sample papers, study material,
or toppers' notes, this PDF has got you covered. Download the Indefinite Integrals now and kickstart your journey towards success in the UPSC exam.
Importance of Indefinite Integrals
The importance of Indefinite Integrals cannot be overstated, especially for UPSC aspirants.
This document holds the key to success in the UPSC exam.
It offers a detailed understanding of the concept, providing invaluable insights into the topic.
By knowing the concepts well in advance, students can plan their preparation effectively.
Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.
Indefinite Integrals Notes
Indefinite Integrals Notes offer in-depth insights into the specific topic to help you master it with ease.
This comprehensive document covers all aspects related to Indefinite Integrals.
It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation.
Practice papers and question papers enable you to assess your progress effectively.
Additionally, the paper analysis provides valuable tips for tackling the exam strategically.
Access to Toppers' notes gives you an edge in understanding complex concepts.
Whether you're a beginner or aiming for advanced proficiency, Indefinite Integrals Notes on EduRev are your ultimate resource for success.
Indefinite Integrals UPSC Questions
The "Indefinite Integrals UPSC Questions" guide is a valuable resource for all aspiring students preparing for the
UPSC exam. It focuses on providing a wide range of practice questions to help students gauge
their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation.
The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level.
Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.
Study Indefinite Integrals on the App
Students of UPSC can study Indefinite Integrals alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the Indefinite Integrals,
students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc.
The EduRev App will make your learning easier as you can access it from anywhere you want.
The content of Indefinite Integrals is prepared as per the latest UPSC syllabus.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup