NCERT Solutions for Class 12 Maths Chapter 7 Integrals have been designed by subject experts at ANAND CLASSES’S to help the students in their board exam preparations This chapter deals with definite and indefinite integrals. Integration class 12 also includes elementary properties of integration including basic techniques of integration. NCERT Class 12 maths chapter 7 solutions will be very helpful when you are solving the questions from NCERT books for Class 12 Maths. These NCERT Class 12 Maths solutions chapter 7 are prepared by subject matter experts that are very easy to understand. students can practice integrals class 12 ncert solutions to get good hold on the concepts.

Download the PDF of NCERT Solutions for Class 12 Maths Chapter 7 – Integrals

Class 12 Maths NCERT Solutions Chapter 7 Integrals

NCERT Solutions for Class 12 Maths Chapter 7 Integrals: Integral calculus emerged as a discipline in response to two distinct problem categories. The first involves determining a function when its derivative is known, while the second centers on calculating the area enclosed by a function’s graph within specific constraints. These two problem types gave rise to the concept of integrals, which manifest in two principal forms: indefinite and definite integrals. Together, these integral forms constitute the field of Integral Calculus.

The major concepts of Maths covered in Chapter 7 – Integrals of NCERT Solutions for Class 12 include

• 7.1 Introduction
• 7.2 Integration as an Inverse Process of Differentiation
• 7.2.1 Geometrical interpretation of indefinite integral
• 7.2.2 Some properties of indefinite integral
• 7.2.3 Comparison between differentiation and integration
• 7.3 Methods of Integration
• 7.3.1 Integration by substitution
• 7.3.2 Integration using trigonometric identities
• 7.4 Integrals of Some Particular Functions
• 7.5 Integration by Partial Fractions
• 7.6 Integration by Parts
• 7.7 Definite Integral
• 7.7.1 Definite integral as the limit of a sum
• 7.8 Fundamental Theorem of Calculus
• 7.8.1 Area function
• 7.8.2 First fundamental theorem of integral calculus
• 7.8.3 Second fundamental theorem of integral calculus
• 7.9 Evaluation of Definite Integrals by Substitution
• 7.10 Some Properties of Definite Integrals

Exercise-wise NCERT Solutions for Class 12 Maths Chapter 7

Exercise 7.1 Solutions 22 Questions

Exercise 7.2 Solutions 39 Questions

Exercise 7.3 Solutions 24 Questions

Exercise 7.4 Solutions 25 Questions

Exercise 7.5 Solutions 23 Questions

Exercise 7.6 Solutions 24 Questions

Exercise 7.7 Solutions 11 Questions

Exercise 7.8 Solutions 6 Questions

Exercise 7.9 Solutions 22 Questions

Exercise 7.10 Solutions 10 Questions

Exercise 7.11 Solutions 21 Questions

Miscellaneous Exercise on Chapter 7 Solutions 44 Questions

Highlights of NCERT Solutions for Class 12 Maths Chapter 7 – Integrals

• The chapter has a total of 42 solved examples
• There are 9 excercise sections in the chapter namely, 7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7, 7.8 and 7.9
• There are a total of 40 Miscellaneous Exercise given at the end of the chapter

Features of NCERT Solutions for Class 12 Maths Chapter 7 Integrals

NCERT has provided ample solved examples and exercise questions for students to practise. Each NCERT 12th Maths Chapter 7 Integrals solution has been prepared to ensure that students understand and retain the concept very well.

Learning the NCERT Solutions of chapter Integrals enables students to study the following:

Integration as the inverse process of differentiation, Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals.

Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.

Frequently Asked Questions on NCERT Solutions for Class 12 Maths Chapter 7

Q1

What is the meaning of integrals in NCERT Solutions for Class 12 Maths Chapter 7?

The area under a curve is often referred to as integral in Calculus. It can be represented on a graph as a mathematical function. A list of important formulas for determining the integration of various functions is covered in this chapter. Integral is also known as antiderivative, and we also know that integration formulas of some functions are the reverse of their differentiation formulas. This chapter is also considered to be one of the important chapters from the exam point of view.

Q2

Is Chapter 7 of NCERT Solutions for Class 12 Maths difficult to understand?

No, Chapter 7 of NCERT Solutions for Class 12 Maths is not difficult to understand. It is one of the interesting topics in Class 12, which will be continued at higher levels of education also. Good knowledge of integral formulas will make it easier for the students to solve the basic sums of integration efficiently. Proper knowledge of derivatives is necessary to understand the concepts of integral calculus without any difficulty.

Q3

Where can I download the NCERT Solutions for Class 12 Maths Chapter 7 PDF online?

You can find the NCERT Solutions for Class 12 Maths Chapter 7 on ANAND CLASSES’S. The solutions are prepared by highly experienced faculty having vast conceptual knowledge. These are considered to be one of the best solutions available online. All the problems from the NCERT textbook are solved step-wise, based on the latest syllabus and the exam pattern designed by the CBSE board.

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