JEE Exam > JEE Notes > Mathematics (Maths) Class 12 > NCERT Solutions Exercise- 7.5: Integrals
NCERT Solutions Class 12 Maths Chapter 7 - Integrals
| Download, print and study this document offline |
Please wait while the PDF view is loading
Page 1 1 / 2 9 N C E R T s o l u t i o n C h a p t e r - 7 I n t e g r a l s - E x e r c i s e 7 . 5 I n t e g r a t e t h e ( r a t i o n a l ) f u n c t i o n i n E x e r c i s e s 1 t o 6 . 1 . A n s . . . . . . . . ( i ) C o m p a r i n g c o e f f i c i e n t s o f o n b o t h s i d e s A + B = 1 . . . . . ( i i ) C o m p a r i n g c o n s t a n t s 2 A + B = 0 . . . . . ( i i i ) S o l v i n g e q . ( i i ) a n d ( i i i ) , w e g e t A = a n d B = 2 P u t t i n g t h e s e v a l u e s o f A a n d B i n e q . ( i ) , = Page 2 1 / 2 9 N C E R T s o l u t i o n C h a p t e r - 7 I n t e g r a l s - E x e r c i s e 7 . 5 I n t e g r a t e t h e ( r a t i o n a l ) f u n c t i o n i n E x e r c i s e s 1 t o 6 . 1 . A n s . . . . . . . . ( i ) C o m p a r i n g c o e f f i c i e n t s o f o n b o t h s i d e s A + B = 1 . . . . . ( i i ) C o m p a r i n g c o n s t a n t s 2 A + B = 0 . . . . . ( i i i ) S o l v i n g e q . ( i i ) a n d ( i i i ) , w e g e t A = a n d B = 2 P u t t i n g t h e s e v a l u e s o f A a n d B i n e q . ( i ) , = 2 / 2 9 = 2 . A n s . = = = 3 . A n s . = . . . . . . . ( i ) C o m p a r i n g c o e f f i c i e n t s o f : A + B + C = 0 . . . . . . . ( i i ) Page 3 1 / 2 9 N C E R T s o l u t i o n C h a p t e r - 7 I n t e g r a l s - E x e r c i s e 7 . 5 I n t e g r a t e t h e ( r a t i o n a l ) f u n c t i o n i n E x e r c i s e s 1 t o 6 . 1 . A n s . . . . . . . . ( i ) C o m p a r i n g c o e f f i c i e n t s o f o n b o t h s i d e s A + B = 1 . . . . . ( i i ) C o m p a r i n g c o n s t a n t s 2 A + B = 0 . . . . . ( i i i ) S o l v i n g e q . ( i i ) a n d ( i i i ) , w e g e t A = a n d B = 2 P u t t i n g t h e s e v a l u e s o f A a n d B i n e q . ( i ) , = 2 / 2 9 = 2 . A n s . = = = 3 . A n s . = . . . . . . . ( i ) C o m p a r i n g c o e f f i c i e n t s o f : A + B + C = 0 . . . . . . . ( i i ) 3 / 2 9 C o m p a r i n g c o e f f i c i e n t s o f : – 5 A – 4 B – 3 C = 3 5 A + 4 B + 3 C = – 3 . . . . . . . ( i i i ) C o m p a r i n g c o n s t a n t s : 6 A + 3 B + 2 C = – 1 . . . . . . . ( i v ) O n s o l v i n g e q . ( i ) , ( i i ) a n d ( i i i ) , w e g e t A = 1 , B = – 5 , C = 4 P u t t i n g t h e v a l u e s o f A , B a n d C i n e q . ( i ) , = = = 4 . A n s . = . . . . . . . ( i ) Page 4 1 / 2 9 N C E R T s o l u t i o n C h a p t e r - 7 I n t e g r a l s - E x e r c i s e 7 . 5 I n t e g r a t e t h e ( r a t i o n a l ) f u n c t i o n i n E x e r c i s e s 1 t o 6 . 1 . A n s . . . . . . . . ( i ) C o m p a r i n g c o e f f i c i e n t s o f o n b o t h s i d e s A + B = 1 . . . . . ( i i ) C o m p a r i n g c o n s t a n t s 2 A + B = 0 . . . . . ( i i i ) S o l v i n g e q . ( i i ) a n d ( i i i ) , w e g e t A = a n d B = 2 P u t t i n g t h e s e v a l u e s o f A a n d B i n e q . ( i ) , = 2 / 2 9 = 2 . A n s . = = = 3 . A n s . = . . . . . . . ( i ) C o m p a r i n g c o e f f i c i e n t s o f : A + B + C = 0 . . . . . . . ( i i ) 3 / 2 9 C o m p a r i n g c o e f f i c i e n t s o f : – 5 A – 4 B – 3 C = 3 5 A + 4 B + 3 C = – 3 . . . . . . . ( i i i ) C o m p a r i n g c o n s t a n t s : 6 A + 3 B + 2 C = – 1 . . . . . . . ( i v ) O n s o l v i n g e q . ( i ) , ( i i ) a n d ( i i i ) , w e g e t A = 1 , B = – 5 , C = 4 P u t t i n g t h e v a l u e s o f A , B a n d C i n e q . ( i ) , = = = 4 . A n s . = . . . . . . . ( i ) 4 / 2 9 C o m p a r i n g c o e f f i c i e n t s o f : A + B + C = 0 . . . . . . . ( i i ) C o m p a r i n g c o e f f i c i e n t s o f : – 5 A – 4 B – 3 C = 1 5 A + 4 B + 3 C = – 1 . . . . . . . ( i i i ) C o m p a r i n g c o n s t a n t s : 6 A + 3 B + 2 C = 0 . . . . . . . ( i v ) O n s o l v i n g e q . ( i ) , ( i i ) a n d ( i i i ) , w e g e t A = B = – 2 , C = P u t t i n g t h e v a l u e s o f A , B a n d C i n e q . ( i ) , = = = 5 . Page 5 1 / 2 9 N C E R T s o l u t i o n C h a p t e r - 7 I n t e g r a l s - E x e r c i s e 7 . 5 I n t e g r a t e t h e ( r a t i o n a l ) f u n c t i o n i n E x e r c i s e s 1 t o 6 . 1 . A n s . . . . . . . . ( i ) C o m p a r i n g c o e f f i c i e n t s o f o n b o t h s i d e s A + B = 1 . . . . . ( i i ) C o m p a r i n g c o n s t a n t s 2 A + B = 0 . . . . . ( i i i ) S o l v i n g e q . ( i i ) a n d ( i i i ) , w e g e t A = a n d B = 2 P u t t i n g t h e s e v a l u e s o f A a n d B i n e q . ( i ) , = 2 / 2 9 = 2 . A n s . = = = 3 . A n s . = . . . . . . . ( i ) C o m p a r i n g c o e f f i c i e n t s o f : A + B + C = 0 . . . . . . . ( i i ) 3 / 2 9 C o m p a r i n g c o e f f i c i e n t s o f : – 5 A – 4 B – 3 C = 3 5 A + 4 B + 3 C = – 3 . . . . . . . ( i i i ) C o m p a r i n g c o n s t a n t s : 6 A + 3 B + 2 C = – 1 . . . . . . . ( i v ) O n s o l v i n g e q . ( i ) , ( i i ) a n d ( i i i ) , w e g e t A = 1 , B = – 5 , C = 4 P u t t i n g t h e v a l u e s o f A , B a n d C i n e q . ( i ) , = = = 4 . A n s . = . . . . . . . ( i ) 4 / 2 9 C o m p a r i n g c o e f f i c i e n t s o f : A + B + C = 0 . . . . . . . ( i i ) C o m p a r i n g c o e f f i c i e n t s o f : – 5 A – 4 B – 3 C = 1 5 A + 4 B + 3 C = – 1 . . . . . . . ( i i i ) C o m p a r i n g c o n s t a n t s : 6 A + 3 B + 2 C = 0 . . . . . . . ( i v ) O n s o l v i n g e q . ( i ) , ( i i ) a n d ( i i i ) , w e g e t A = B = – 2 , C = P u t t i n g t h e v a l u e s o f A , B a n d C i n e q . ( i ) , = = = 5 . 5 / 2 9 A n s . = = = = . . . . ( i ) C o m p a r i n g c o e f f i c i e n t s o f o n b o t h s i d e s A + B = 2 . . . . . . . ( i i ) C o m p a r i n g c o n s t a n t s 2 A + B = 0 . . . . . ( i i i ) S o l v i n g e q . ( i i ) a n d ( i i i ) , w e g e t A = a n d B = 4 P u t t i n g t h e s e v a l u e s o f A a n d B i n e q . ( i ) ,Read More
|
204 videos|290 docs|139 tests
|
FAQs on NCERT Solutions Class 12 Maths Chapter 7 - Integrals
| 1. What are integrals? |  |
Ans. Integrals are mathematical tools used to calculate the area under a curve or to find the accumulation of quantities over a given interval. They are fundamental in calculus and have various applications in physics, engineering, economics, and other fields.
| 2. How do you find the integral of a function? | |
Ans. To find the integral of a function, you can use integration techniques such as the power rule, substitution, integration by parts, or trigonometric substitutions. These techniques allow you to manipulate the function and evaluate the integral using specific formulas or rules.
| 3. What is the difference between definite and indefinite integrals? | |
Ans. A definite integral has upper and lower limits that define a specific interval over which the integration is performed. It gives a numerical value representing the area or accumulation within that interval. On the other hand, an indefinite integral does not have any limits and represents a family of functions obtained by adding a constant (known as the constant of integration) to the result.
| 4. Can integrals be used to solve real-life problems? | |
Ans. Yes, integrals are widely used to solve real-life problems. For example, they can be used to calculate the area under a curve, which can represent the total distance traveled, the total amount of a substance dissolved, or the total revenue generated over a given time period. Integrals are also used in physics to calculate quantities such as work, fluid flow, or electric charge.
| 5. What are the applications of integrals in engineering? | |
Ans. Integrals have various applications in engineering. They can be used to determine the moment of inertia of a solid object, calculate the displacement and velocity of a particle, find the center of mass of a system, analyze electrical circuits, and solve differential equations that model physical systems. These applications help engineers in designing and optimizing structures, systems, and processes.
Related Exams
About this Document
|
4K Views |
|
4.73/5 Rating |
|
Dec 22, 2024 Last updated |
Document Description: NCERT Solutions Exercise- 7.5: Integrals for JEE 2024 is part of Mathematics (Maths) Class 12 preparation.
The notes and questions for NCERT Solutions Exercise- 7.5: Integrals have been prepared according to the JEE exam syllabus. Information about NCERT Solutions Exercise- 7.5: Integrals covers topics
like and NCERT Solutions Exercise- 7.5: Integrals Example, for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for NCERT Solutions Exercise- 7.5: Integrals.
Introduction of NCERT Solutions Exercise- 7.5: Integrals in English is available as part of our Mathematics (Maths) Class 12
for JEE & NCERT Solutions Exercise- 7.5: Integrals in Hindi for Mathematics (Maths) Class 12 course.
Download more important topics related with notes, lectures and mock test series for JEE
Exam by signing up for free. JEE: NCERT Solutions Class 12 Maths Chapter 7 - Integrals
Description
Full syllabus notes, lecture & questions for NCERT Solutions Class 12 Maths Chapter 7 - Integrals - JEE | Plus excerises question with solution to help you revise complete syllabus for Mathematics (Maths) Class 12 | Best notes, free PDF download
Information about NCERT Solutions Exercise- 7.5: Integrals
In this doc you can find the meaning of NCERT Solutions Exercise- 7.5: Integrals defined & explained in the simplest way possible. Besides explaining types of
NCERT Solutions Exercise- 7.5: Integrals theory, EduRev gives you an ample number of questions to practice NCERT Solutions Exercise- 7.5: Integrals tests, examples and also practice JEE
tests
|
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
Free
,video lectures
,Semester Notes
,Exam
,NCERT Solutions Class 12 Maths Chapter 7 - Integrals
,mock tests for examination
,NCERT Solutions Class 12 Maths Chapter 7 - Integrals
,past year papers
,Sample Paper
,practice quizzes
,NCERT Solutions Class 12 Maths Chapter 7 - Integrals
,ppt
,study material
,MCQs
,Extra Questions
,Previous Year Questions with Solutions
,shortcuts and tricks
,Important questions
,Viva Questions
,Summary
,Objective type Questions
;
Additional Information about NCERT Solutions Exercise- 7.5: Integrals for JEE Preparation
NCERT Solutions Exercise- 7.5: Integrals Free PDF Download
The NCERT Solutions Exercise- 7.5: 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 NCERT Solutions Exercise- 7.5: Integrals now and kickstart your journey towards success in the JEE exam.
Importance of NCERT Solutions Exercise- 7.5: Integrals
The importance of NCERT Solutions Exercise- 7.5: 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.
NCERT Solutions Exercise- 7.5: Integrals Notes
NCERT Solutions Exercise- 7.5: 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 NCERT Solutions Exercise- 7.5: 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, NCERT Solutions Exercise- 7.5: Integrals Notes on EduRev are your ultimate resource for success.
NCERT Solutions Exercise- 7.5: Integrals JEE Questions
The "NCERT Solutions Exercise- 7.5: 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 NCERT Solutions Exercise- 7.5: Integrals on the App
Students of JEE can study NCERT Solutions Exercise- 7.5: Integrals alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the NCERT Solutions Exercise- 7.5: 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 NCERT Solutions Exercise- 7.5: Integrals is prepared as per the latest JEE syllabus.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup