# NCERT Exemplar Class 12 Maths Solutions Chapter 7 Integrals

**NCERT exemplar Class 12 Maths solutions chapter 7** Integrals is one of the most important subjects for those who want to prepare for the advanced levels of Mathematics and also want to score higher in their exams, studying this chapter is crucial. The NCERT Exemplar solutions for Class 12 Maths chapter 7 holds major importance in both board exams of CBSE and also in competitive exams. Students can utilize the NCERT exemplar Class 12 Maths solutions chapter 7 PDF download function to download the solutions and make learning even more convenient and easy to follow and understand

**Latest Updates for CBSE Class 12th **

**10 Feb 2023:****Over Rs 2,000 crore cut from 12 scholarship:****Check details here****02 Jan 2023:**CBSE has revised the CBSE Class 12 board date sheet 2023. Check new exam dates here.

**29 Dec 2022:**CBSE datesheet 2023 released for theory exams; Check exam dates here.

Stay up-to date with CBSE Class 12th News

Question:30

Answer:

By applying partial fraction;

By applying the given limits 0 to π/2

Question:43

Evaluate the following:

(Hint: Put )

Answer:

Given:

Put

Taking out common in both the numerators

Put (2) and (3) in (1)

Question:44

Evaluate the following:

(Hint: Divide Numerator and Denominator by )

Answer:

Given:

Dividing Numerator and Denominator by

Question:53

Answer:

C)

Given:

Using concept of partial fractions

On solving the above three equations we get

On comparing (1) and (2) we get,

Question:63

Fill in the blanks in each of the following

The value of is ____________.

Answer:

0

Using the property:

**More About NCERT Exemplar Class 12 Maths Solutions Chapter 7 Integrals**

Calculus can pose to be a difficult part of mathematics for many, but if one knows what to study and how to study then it can be simplified easily. NCERT exemplar Class 12 Maths solutions chapter 7 are not only crucial for mathematics and higher education point of view. It is also one of the highly scoring chapters of NCERT Class 12 Maths Solutions.

But it is also needed to study physics. In physics integrals play a major role, as it is used in topics like gravitation, work, probability, kinetic energy etc. therefore, the students must pay attention to what integrals are and how it is applied.

**NCERT Exemplar Solutions For Class 12 Maths Chapter 7 Integrals Sub-Topics Covered**

The sub topics covered in NCERT exemplar Class 12 Maths chapter 7 solutions are:

- Introduction

- Integration as an inverse process of differentiation

- Geometric interpretation of indefinite integral
- Some properties of indefinite integral
- Comparison between integration and differentiation

- Methods of integration

- Integration by substitution
- Integration by trigonometric identities

- Integrals of some particular functions

- Integration of partial functions

- Integration by parts

- Integral of the typefxf'xdx
- Integral of some other types

- Definite integrals

- Definite integral as a limit of a sum

- The fundamental theorem of calculus

- Area function
- First fundamental theorem of integral calculus
- Second fundamental theorem of integral calculus

- Evaluation of definite integrals by substitution

- Some properties of definite integrals

**What can you learn in Class 12 Maths NCERT Exemplar Solutions Chapter 7?**

In NCERT exemplar Class 12 Mathematics chapter 7 Integrals, students will get a better picture of what are integrals and how it is used in advanced calculus. Here, they will learn about integration and geometric representation of the same using graphs. One will learn in detail about various methods of integration, the difference between differentiation and integration, and indefinite integral properties.

Many students tend to find integrals as a chapter that is difficult and hassling. But they should remember that if one wants to score well in exams and also pursue a career in engineering, then understanding and studying integrals is crucial. Therefore, one should ask as many questions as possible to get a hang of the topic.

NCERT exemplar solutions for Class 12 Maths chapter 7 will help in tackling the questions asked in this topic. One should practice the questions as much as possible and should use the Class 12 Maths NCERT exemplar solutions chapter 7 as reference. This will not only make the student confident about integrals but also for tackling any numerical they get in the exam.

**NCERT Exemplar Class 12 Maths Solutions**

**Benefits of NCERT Exemplar Class 12 Maths Solutions Chapter 7**

- In NCERT exemplar Class 12 Maths solutions chapter 7, there are a variety of concepts and topics covered. The main aim is to make the students well aware of integrals and its operations, so much so that any question can be solved easily. Students will learn how to find integrals for various types of functions.
- Integrals are the opposite of derivatives of a function and are denoted by the area under the function curve. When it comes to integrals, it can be stated as the opposite of differential calculus. In simple words, integrals describe the numerical value of any type of change like distance like displacement, volume, area and work.
- NCERT exemplar Class 12 Maths chapter 7 solutions deals with the important topics coming for the exams which are the methods, functions and operations.

**NCERT Exemplar Class 12 Solutions**

### Also, check NCERT Solutions for questions given in the book:

Chapter 1 | |

Chapter 2 | |

Chapter 3 | |

Chapter 4 | |

Chapter 5 | |

Chapter 6 | |

Chapter 7 | Integrals |

Chapter 8 | |

Chapter 9 | |

Chapter 10 | |

Chapter 11 | |

Chapter 12 | |

Chapter 13 |

#### Must Read NCERT Solution subject wise

- NCERT Solution for Class 12 Physics
- NCERT Solution for Class 12 Chemistry
- NCERT Solution for Class 12 Maths
- NCERT Solution for Class 12 Biology

#### Read more NCERT Notes subject wise

- NCERT Notes for Class 12 Physics
- NCERT Notes for Class 12 Chemistry
- NCERT Notes for Class 12 Maths
- NCERT Notes for Class 12 Biology

#### Also Check NCERT Books and NCERT Syllabus here

## Frequently Asked Question (FAQs) - NCERT Exemplar Class 12 Maths Solutions Chapter 7 Integrals

**Question: **How many times should one need to read the NCERT books?

**Answer: **

Students should read the books enough times months before your exam for better remembering. They can also take help of NCERT exemplar Class 12 Maths solutions chapter 7 pdf download using an online webpage to pdf tool.

**Question: **How many questions are there in this chapter?

**Answer: **

The NCERT exemplar solutions for Class 12 Maths chapter 7 consists of 1 exercise with 63 distinct questions for practice.

**Question: **What are the important topics of this chapter?

**Answer: **

Methods of Integration, Integration by Parts and Fundamental Theorem of Calculus are some of the important topics of this chapter. However, rest should not be neglected either.

## Latest Articles

##### Kendriya Vidyalaya Admission 2023 for Class 1 - Check Admissio...

KVS Admission 2023 for Class 1 - Kendriya Vidyalaya Sangathan...

##### Kendriya Vidyalaya Admission 2023-24 - Eligibility, Dates, Exa...

Kendriya Vidyalaya Admission 2023-24 - Know about KV admission...

##### Kendriya Vidyalaya Admission Form 2023 - Fill KVS Admission Fo...

Kendriya vidyalaya admission form 2023 - Kendriya vidyalaya sa...

##### NVS Admit Card 2023 for Class 6 & 9 (Released) - Know How to D...

NVS Admit Card 2023 Class 6 & 9 - Navodaya Vidyalaya Samiti ha...

##### Navodaya Exam Date 2023 Class 6 & 9- Application Form, Admit C...

Navodaya exam date 2023 class 6 & 9- Navodaya Vidyalaya Samiti...

##### Navodaya Answer Key 2023 Class 9 - Download JNVST Class 9 Answ...

Navodaya Answer Key 2023 Class 9 - JNVST Class 9 2023 answer k...

##### NVS Admission Class 9 2023 - Apply for Navodaya Vidyalaya 9 Ad...

NVS admission class 9 2023- Students can fill the Navodaya ad...

##### Navodaya Result 2023 Class 6 & 9 - JNV Result 2023 at navodaya...

Jawahar Navodaya Result 2023 Class 6 & 9 - Navodaya Vidyalaya ...

##### Sainik School Cut Off Marks 2023 Class 6 & 9 - Check AISSEE Ex...

Sainik School Cutoff Marks 2023 - National Testing Agency has ...

##### Sainik School Result 2023 for Class 6 & 9 - Check AISSEE Merit...

Sainik school result 2023 Class 6 & 9 - National Testing Agenc...

## Explore Popular Degree, Branches and Courses

### Browse by Degrees

### Browse by Branches/Majors

## Questions related to CBSE Class 12th

### i couldnt clear 1st compartment (which held in August 2022) cbse class 12th so can I give improvement in all subjects which to be held on March 2023. tell me a solution i need more than 75% in class 12th

hello,

Yes you can appear for the compartment paper again since CBSE gives three chances to a candidate to clear his/her exams so you still have two more attempts. However, you can appear for your improvement paper for all subjects but you cannot appear for the ones in which you have failed.

I hope this was helpful!

Good Luck

### i was not able to clear 1st compartment and now I have to give 2nd compartment so can I give improvement exam next year? plz tell me very much tensed(cbse class 12th)

Hello dear,

If you was not able to clear 1st compartment and now you giving second compartment so YES, you can go for your improvement exam next year but if a student receives an improvement, they are given the opportunity to retake the boards as a private candidate the following year, but there are some requirements. First, the student must pass all of their subjects; if they received a compartment in any subject, they must then pass the compartment exam before being eligible for the improvement.

As you can registered yourself as private candidate for giving your improvement exam of 12 standard CBSE(Central Board of Secondary Education).For that you have to wait for a whole year which is bit difficult for you.

Positive side of waiting for whole year is you have a whole year to preparing yourself for your examination. You have no distraction or something which may causes your failure in the exams. In whole year you have to stay focused on your 12 standard examination for doing well in it. By this you get a highest marks as a comparison of others.

Believe in Yourself! You can make anything happen

All the very best.

### if i am giving improvement in one subject this year, will i be able to give improvement in more subjects next year?

Hello Student,

I appreciate your Interest in education. See the improvement is not restricted to one subject or multiple subjects and we cannot say if improvement in one subject in one year leads to improvement in more subjects in coming year.

You just need to have a revision of all subjects what you have completed in the school. have a revision and practice of subjects and concepts helps you better.

All the best.

### I got an RT for 2 subjects, so do I have to give exams for all the subjects in the coming year or just the 2. pls help me

Hi,

You just need to give the exams for the concerned two subjects in which you have got RT. There is no need to give exam for all of your subjects, you can just fill the form for the two subjects only.

### I will have my boards in Feb 2023 (Class 12) and I still havent completed 1 chapter in any subject (Physics, chemistry and maths) , My 11th concepts are not that great but its okish, I wanted to know that If I do start studying from 15th of August Can I get above 85?

If you'll do hard work then by hard work of 6 months you can achieve your goal but you have to start studying for it dont waste your time its a very important year so please dont waste it otherwise you'll regret.