NCERT Solutions Class 12 Mathematics Chapter 8

Integral Calculus is related to Eudoxus’ (440 B.C.) and Archimedes’ (440 B.C.) exhaustion approach (300 B.C.). This method emerged from the need to solve problems estimating the areas of plane figures, surface areas, and solid body volumes. Newton began working on Calculus in 1665, which led to the formulation of concepts as we know them. NCERT solutions class 12 mathematics chapter 8 provides various hints, tactics, and intriguing facts to help students break up the monotony of studying and develop a mathematical base that will help them throughout their studies.

NCERT solutions class 12 mathematics chapter 8 – Application of Integrals is a continuation of the previous chapter, in which students learned about integration and how to solve problems using various methods. Students have learnt formulae for calculating the areas of triangles, rectangles, trapeziums, and circles, among other geometrical figures. These fundamental formulae are crucial in applying mathematics to a wide range of real-world issues. However, this method fails when estimating the areas encompassed by curves. Integral calculus is required to calculate the areas under a curve. NCERT solutions class 12 mathematics chapter 8 use integrals to get the area under curves. Curves such as circles, parabolas, and hyperbolas can be simple or complex.

Key Topics Covered in NCERT Solutions Class 12 Mathematics Chapter 8

All the topics covered in NCERT Solutions Class 12 Mathematics Chapter 8 are equally important. They go over many aspects of integration and how to calculate the area under a curve throughout multiple scenarios. Before attempting the practice questions, students must first grasp the underlying concepts. They should also be familiar with the preceding chapter and the formulas listed. The  NCERT Solutions Class 12 Mathematics Chapter 8 broadly covers two main concepts of the chapter ‘Application of Integrals’ and  ‘Integral Calculus’.

List of NCERT Solutions Class 12 Mathematics Chapter 8 Exercises

Students learned about definite integrals as the limit of a sum in Chapter 7 and how to evaluate them using the Fundamental Theorem of Calculus. This concept is used in NCERT solutions for class 12 mathematics chapter 8 to give students an easy approach to computing the area under curves. The area beneath the curve can be thought of as a collection of several very thin vertical stripes. We may now determine the total area necessary by integrating this region between some specific limitations. NCERT Solutions for class 12 mathematics chapter 8 Application of Integrals gives students a better grasp of integration using real-life examples. We’ll look at a range of examples, formulas, and theories in depth in this article to help students create a strong mathematical foundation.

Several formulas and theorems are used in this lesson. There is also a blend of current topics with those that the students learned in the previous chapter. If not approached systematically, integration can become a difficult and perplexing concept. Students must regularly review this lesson for all these reasons, particularly the formulas, to learn the material. With the help of examples and practice problems, all the tasks in NCERT Solutions Class 12 Mathematics Chapter 8 – Application of Integrals are well explained. Here are some NCERT solutions for students to practise –

 Class 12 Mathematics Chapter 8 – Ex 8.1 Solutions – 13 Questions

Class 12 Mathematics Chapter 8 – Ex 8.2 Solutions – 7 Questions

Class 12 Mathematics Chapter 8 Miscellaneous Ex – 19 Questions

The area bounded by the curve of a function, the area between two curves, and the area under simple curves are all covered in NCERT solutions class 12 mathematics chapter 8.

NCERT Solutions Class 12 Mathematics Chapter 8 Formula List

NCERT solutions class 12 mathematics chapter 8 requires using formulas and a constant focus. Students must comprehend what the question requires and carry out the procedures stepwise. They should also divide the problem into smaller parts to make it easier to understand and avoid ambiguity, hence lowering the risk of errors. More significantly, children must understand the processes in the technique since they are the keys to answering a variety of questions.

The following are some formulas that are regularly used in NCERT solutions for class 12 mathematics chapter 8 –

• Area of the region bounded by the curve y = f (x), x-axis and the lines x = a and x = b (b > a) : a∫by dx = a∫bf(x) dx.
• The area of the region bounded by the curve x = φ (y), y-axis and the lines y = c, y = d : c∫d x dy = c∫d φ (y) dy.
• The area of the region enclosed between two curves y = f (x), y = g (x) and the lines x = a, x = b : b∫a[f(x) – g(x)] dx.

Class 12 NCERT Mathematics Syllabus

Term – 1

 Term – 2

Experts at Extramarks create NCERT Solutions to assist students to understand ideas more quickly and correctly. NCERT Solutions provide extensive, step-by-step explanations of textbook problems. All classes can benefit from such solutions –

• NCERT Solutions class 1
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• NCERT Solutions class 12

NCERT Mathematics Exam Pattern

Key Features of NCERT Solutions Class 12 Mathematics Chapter 8

To do well in CBSE and pass various competitive exams such as NEET and IIT, one must have a strong mathematical foundation. The NCERT books present you with difficult problems that improve your analytical ability and expose you to many questions that could appear in all of these exams. Our integrals class 12 solutions adhere to the most recent CBSE curriculum and are incredibly valuable to your preparation for the following reasons:

• The answers are exceptional because teachers with deep subject knowledge create them.
• You can revise all the significant points of a chapter in a short amount of time.
• The solutions also prepare you for managing your stress and time, giving you a better chance of finishing your examinations on time.
• NCERT solutions class 12 mathematics chapter 8 will assist you in grasping the fundamental concepts quickly and easily.

NCERT Exemplar Class 12 Mathematics 

Here are some solutions and problems to help students prepare for their final exams. These example questions are a little more complex, and they cover a variety of concepts in each chapter of Class 12 Mathematics subject. Students will fully understand all the concepts covered in each chapter by practising these NCERT Exemplars for mathematics Class 12. Each question in these materials is connected to concepts covered in the CBSE Class 12 syllabus (2022-2023). Our experts provide the best solutions to challenges that students confront. To match the ideas taught in each class and provide the greatest practising materials or worksheets for students, all these questions reflect the question pattern found in NCERT books.