JEE Exam > JEE Notes > Mathematics (Maths) for JEE Main & Advanced > Flashcards: Definite Integrals
Flashcards: Definite Integrals | Mathematics (Maths) for JEE Main & Advanced PDF Download
| Download, print and study this document offline |
Please wait while the PDF view is loading
Page 1 DEFINITE INTEGRAL Here we shall define integration as a process of summation or define integral as the limit of a sum. Then we discuss some properties of definite integral. The concept of definite integral is then used to find the area enclosed by certain curves. Page 2 DEFINITE INTEGRAL Here we shall define integration as a process of summation or define integral as the limit of a sum. Then we discuss some properties of definite integral. The concept of definite integral is then used to find the area enclosed by certain curves. Fundamental theorem of calculus Let ?? ( ?? ) be a continuous real valued function defined on [ ?? , ?? ] such that ? ?? ( ?? ) ???? = ?? ( ?? ) + ?? . Then ? ?? ?? ? ?? ( ?? ) ???? = ?? ( ?? ) - ?? ( ?? ), called definite integral of ?? ( ?? ) in [ ?? , ?? ]. Page 3 DEFINITE INTEGRAL Here we shall define integration as a process of summation or define integral as the limit of a sum. Then we discuss some properties of definite integral. The concept of definite integral is then used to find the area enclosed by certain curves. Fundamental theorem of calculus Let ?? ( ?? ) be a continuous real valued function defined on [ ?? , ?? ] such that ? ?? ( ?? ) ???? = ?? ( ?? ) + ?? . Then ? ?? ?? ? ?? ( ?? ) ???? = ?? ( ?? ) - ?? ( ?? ), called definite integral of ?? ( ?? ) in [ ?? , ?? ]. Remark: 1 If ?? ( ?? ) is discontinuous at ?? = ?? and continuous at ?? = ?? then ? ?? ?? ? ?? ( ?? )???? = ?? ( ?? ) - l im ?? ? ?? + ? ?? ( ?? ) 2 If ?? ( ?? ) is discontinuous at ?? = ?? and continuous at ?? = ?? then ? ?? ?? ? ?? ( ?? )???? = l im ?? ? ?? - ? ?? ( ?? ) - ?? ( ?? ) Page 4 DEFINITE INTEGRAL Here we shall define integration as a process of summation or define integral as the limit of a sum. Then we discuss some properties of definite integral. The concept of definite integral is then used to find the area enclosed by certain curves. Fundamental theorem of calculus Let ?? ( ?? ) be a continuous real valued function defined on [ ?? , ?? ] such that ? ?? ( ?? ) ???? = ?? ( ?? ) + ?? . Then ? ?? ?? ? ?? ( ?? ) ???? = ?? ( ?? ) - ?? ( ?? ), called definite integral of ?? ( ?? ) in [ ?? , ?? ]. Remark: 1 If ?? ( ?? ) is discontinuous at ?? = ?? and continuous at ?? = ?? then ? ?? ?? ? ?? ( ?? )???? = ?? ( ?? ) - l im ?? ? ?? + ? ?? ( ?? ) 2 If ?? ( ?? ) is discontinuous at ?? = ?? and continuous at ?? = ?? then ? ?? ?? ? ?? ( ?? )???? = l im ?? ? ?? - ? ?? ( ?? ) - ?? ( ?? ) Remark: 3. If ?? ( ?? ) is discontinuous at ?? = ?? and ?? = ?? then ? ?? ?? ? ?? ( ?? ) ???? = l im ?? ? 0 ? ? ?? + ?? ?? - ?? ? ?? ( ?? )???? or l im ?? ? ?? - ? ?? ( ?? ) - l im ?? ? ?? + ? ?? ( ?? ) 4. If ?? ( ?? ) is discontinuous at ?? = ?? ( ?? < ?? < ?? ) then ? ?? ?? ? ?? ( ?? )???? = l im ?? ? 0 ? ? ?? ?? - ?? ? ?? ( ?? )???? + l im ?? ? 0 ? ? ?? + ?? ?? ? ?? ( ?? ) ???? Page 5 DEFINITE INTEGRAL Here we shall define integration as a process of summation or define integral as the limit of a sum. Then we discuss some properties of definite integral. The concept of definite integral is then used to find the area enclosed by certain curves. Fundamental theorem of calculus Let ?? ( ?? ) be a continuous real valued function defined on [ ?? , ?? ] such that ? ?? ( ?? ) ???? = ?? ( ?? ) + ?? . Then ? ?? ?? ? ?? ( ?? ) ???? = ?? ( ?? ) - ?? ( ?? ), called definite integral of ?? ( ?? ) in [ ?? , ?? ]. Remark: 1 If ?? ( ?? ) is discontinuous at ?? = ?? and continuous at ?? = ?? then ? ?? ?? ? ?? ( ?? )???? = ?? ( ?? ) - l im ?? ? ?? + ? ?? ( ?? ) 2 If ?? ( ?? ) is discontinuous at ?? = ?? and continuous at ?? = ?? then ? ?? ?? ? ?? ( ?? )???? = l im ?? ? ?? - ? ?? ( ?? ) - ?? ( ?? ) Remark: 3. If ?? ( ?? ) is discontinuous at ?? = ?? and ?? = ?? then ? ?? ?? ? ?? ( ?? ) ???? = l im ?? ? 0 ? ? ?? + ?? ?? - ?? ? ?? ( ?? )???? or l im ?? ? ?? - ? ?? ( ?? ) - l im ?? ? ?? + ? ?? ( ?? ) 4. If ?? ( ?? ) is discontinuous at ?? = ?? ( ?? < ?? < ?? ) then ? ?? ?? ? ?? ( ?? )???? = l im ?? ? 0 ? ? ?? ?? - ?? ? ?? ( ?? )???? + l im ?? ? 0 ? ? ?? + ?? ?? ? ?? ( ?? ) ???? Note that even if ?? ( ?? ) is not defined at ?? = ?? or ?? = ?? or at both, ? ?? ?? ? ?? ( ?? )???? can be evaluated. ?? and ?? are called lower and upper limits of integration respectively. If we make change in variable (i.e. substitution) then limit of integration should be changed accordingly.Read More
|
209 videos|443 docs|143 tests
|
About this Document
|
4.92/5 Rating |
|
Dec 18, 2024 Last updated |
Document Description: Flashcards: Definite Integrals for JEE 2024 is part of Mathematics (Maths) for JEE Main & Advanced preparation.
The notes and questions for Flashcards: Definite Integrals have been prepared according to the JEE exam syllabus. Information about Flashcards: Definite Integrals covers topics
like and Flashcards: Definite Integrals Example, for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Flashcards: Definite Integrals.
Introduction of Flashcards: Definite Integrals in English is available as part of our Mathematics (Maths) for JEE Main & Advanced
for JEE & Flashcards: Definite Integrals in Hindi for Mathematics (Maths) for JEE Main & Advanced course.
Download more important topics related with notes, lectures and mock test series for JEE
Exam by signing up for free. JEE: Flashcards: Definite Integrals | Mathematics (Maths) for JEE Main & Advanced
Description
Full syllabus notes, lecture & questions for Flashcards: Definite Integrals | Mathematics (Maths) for JEE Main & Advanced - JEE | Plus excerises question with solution to help you revise complete syllabus for Mathematics (Maths) for JEE Main & Advanced | Best notes, free PDF download
Information about Flashcards: Definite Integrals
In this doc you can find the meaning of Flashcards: Definite Integrals defined & explained in the simplest way possible. Besides explaining types of
Flashcards: Definite Integrals theory, EduRev gives you an ample number of questions to practice Flashcards: Definite Integrals tests, examples and also practice JEE
tests
|
209 videos|443 docs|143 tests
|
Download as PDF
|
Explore Courses for JEE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
Related Searches
Exam
,past year papers
,shortcuts and tricks
,Semester Notes
,Important questions
,Flashcards: Definite Integrals | Mathematics (Maths) for JEE Main & Advanced
,Viva Questions
,study material
,Summary
,Previous Year Questions with Solutions
,Flashcards: Definite Integrals | Mathematics (Maths) for JEE Main & Advanced
,Extra Questions
,practice quizzes
,video lectures
,Sample Paper
,Objective type Questions
,mock tests for examination
,Flashcards: Definite Integrals | Mathematics (Maths) for JEE Main & Advanced
,ppt
,Free
,MCQs
;
Additional Information about Flashcards: Definite Integrals for JEE Preparation
Flashcards: Definite Integrals Free PDF Download
The Flashcards: Definite Integrals is an invaluable resource that delves deep into the core of the JEE 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 Flashcards: Definite Integrals now and kickstart your journey towards success in the JEE exam.
Importance of Flashcards: Definite Integrals
The importance of Flashcards: Definite Integrals cannot be overstated, especially for JEE aspirants.
This document holds the key to success in the JEE 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.
Flashcards: Definite Integrals Notes
Flashcards: Definite 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 Flashcards: Definite 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, Flashcards: Definite Integrals Notes on EduRev are your ultimate resource for success.
Flashcards: Definite Integrals JEE Questions
The "Flashcards: Definite Integrals JEE Questions" guide is a valuable resource for all aspiring students preparing for the
JEE 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 Flashcards: Definite Integrals on the App
Students of JEE can study Flashcards: Definite Integrals alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the Flashcards: Definite 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 Flashcards: Definite Integrals is prepared as per the latest JEE 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