Table of Contents
Subject specialists have created NCERT Exemplar Solutions for Class 12 Maths Chapter 7 Integrals, which includes thorough solutions for reference. All of the questions from the textbook’s exercises are answered here. Students can use these answers to help them prepare for their exams. The NCERT Exemplar Solutions for Class 12 provide useful solutions for improving conceptual knowledge and preparing for exams like JEE.
The solutions are carefully solved using student-friendly terms while still adhering to the norms that must be followed when solving NCERT Exemplar Solutions for Class 12. Practicing these answers can be incredibly advantageous not only in terms of exams but also in terms of helping Class 12 pupils perform well in upcoming competitive exams.
The approaches for answering have been given special consideration to stay on target while not deviating from the intended answer. Because time is so important in exams, excellent time management when answering questions is essential for getting the best results.
The topics and subtopics are listed below:
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
The number of questions in the exercise of NCERT Class 12 Exemplar Solutions for Maths Chapter 7 is given below:
Exercise 7
- 7.1 Solutions 22 Questions
- 7.2 Solutions 39 Questions
- 7.3 Solutions 24 Questions
- 7.4 Solutions 25 Questions
- 7.5 Solutions 23 Questions
- 7.6 Solutions 24 Questions
- 7.7 Solutions 11 Questions
- 7.8 Solutions 6 Questions
- 7.9 Solutions 22 Questions
- 7.10 Solutions 10 Questions
- 7.11 Solutions 21 Questions
- Miscellaneous Exercise On Chapter 7 Solutions 44 Questions
NCERT Exemplar Solutions for Class 12 Maths Chapter 7- Integrals
The chapter Integrals is part of the unit Calculus, which is covered in term II of CBSE Syllabus 2021-22 and accounts for 35 of the total marks. This chapter contains 11 activities as well as a random activity to assist students to understand the idea of Integrals. The following topics are covered in Chapter 7
- Differentiation is the inverse of integration. We are given a function in differential calculus and must discover its derivative or differential, whereas, in integral calculus, we must find a function whose differential is known. As a result, integration is the polar opposite of differentiation.
- An indefinite integral is a collection of curves formed by translating one of the curves parallel to itself upwards or downwards along the y-axis from a geometric perspective.
- Indefinite integrals have a few features.
- Some common integrals
- Partial fractions integration
- Integration by substitution: When the integration variable is changed, an integral is frequently reduced to one of the fundamental integrals. The procedure of substitution is the process of changing one variable to another. We employ certain well-known identities to determine the integrals when the integrand contains some trigonometric functions.
- Integration by parts: the integral of the product of two functions = first function × integral of the second function – integral of {differential coefficient of the first function × integral of the second function}.
- Integral calculus’s first fundamental theorem.
- Integral calculus’ second fundamental theorem.
Students can use the NCERT Exemplar Solutions to help them solve tough questions, clear their doubts, prepare for exams, and revise. Students’ confidence in taking the Class 12 Maths second term test will be boosted by referring to these solutions.
Key Features of NCERT Exemplar Solutions for Class 12 Maths Chapter 7- Integrals
Students can study the following topics by learning the NCERT Exemplar Solutions for chapter Integrals:
As the inverse of differentiation, integration Substitution, partial fractions, and parts are used to integrate a number of functions. Simple integrals of the following categories and problems dependent on them are evaluated.
Fundamental Theorem of Calculus, Definite Integrals as a Limit of a Sum (without proof). Evaluation of definite integrals and basic properties of definite integrals.
Frequently Asked Questions
What is the meaning of integrals in NCERT Exemplar Solutions for Class 12 Maths Chapter 7?
In Calculus, the area under a curve is often referred to as an integral. It can be visualized as a mathematical function on a graph. This chapter contains a list of important formulas for determining the integration of various functions. Integral is also known as antiderivative because we know that some functions' integration formulations are the opposite of their differentiation formulas. This chapter is also regarded as one of the most crucial in terms of exam preparation.
Is Chapter 7 of NCERT Exemplar Solutions for Class 12 Maths difficult to understand?
No, NCERT Exemplar Solutions for Class 12 Maths Chapter 7 is not tough to comprehend. It's one of the more engaging topics in Class 12, and it'll be continuing in higher education as well. Students will be able to answer the basic sums of integration more effectively if they have a good understanding of integral formulas. To grasp the principles of integral calculus without difficulty, you must have a solid understanding of derivatives.
Where can I download the NCERT Exemplar Solutions for Class 12 Maths Chapter 7 PDF online?
Infinity Learn has the NCERT Exemplar Solutions for Class 12 Maths Chapter 7 available. The solutions are created by a highly qualified faculty with a broad conceptual understanding. These are regarded as one of the top-rated options available on the internet. Based on the newest syllabus for 2021-22 and the CBSE board's exam format, all questions from the NCERT textbook are handled in a step-by-step way.
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