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RS Aggarwal Class 12 Chapter 17 Solutions (Area of Bounded Regions)

RS Aggarwal Solutions for Class 12 Chapter 17 ‘Area of Bounded Regions’ is curated to help you grasp the methods employed in this chapter. This chapter is very crucial in many engineering fields and therefore it is a very important part of your syllabus. You will learn about the area between two curves. This chapter of RS Aggarwal Solutions is an application of the integral calculus that we have studied so far. The other topics that are covered in this chapter include the area of an ellipse and how we can apply the concept of area bounded region to check the symmetry of a given curve.

There is 1 exercise consisting of 20 questions to guide you in understanding the topic in a gradual manner. The exercise questions are of all kinds, that is, short answer type as well as long answer type. These exercise solutions demand the core concepts of integration and equation of different kinds of curves such as the ellipse, parabola etc. To be able to solve these questions, the prerequisite is an in-depth knowledge of calculus and functions, of which the perfect guidance you will get at Instasolv.

We, at Instasolv, use research-based analysis on major doubts and frequently asked questions and then sort the queries in a standard way. Solving the questions by taking the reference of Instasolv will help you optimise your study hours. You will also be able to polish your time management skills with the help of these solutions by our maths experts.

Topics Covered in RS Aggarwal Solutions for Class 12 Chapter 17 – Area of Bounded Regions

Introduction:

Integration is calculating the area by splitting the required region to an infinite number of smaller areas and then adding up these areas. 

Area Between Two Curves:

Case 1: Let two curves be y=f(x) and y=g(x), given that, f(x) ≥ g(x) in [a,b]. In the given case, the point of intersection of these two curves can be given as x=a and x=b, by obtaining the given values of y from the equation of the two curves.

Our aim is to find the enclosed area between the two given curves. To find this area, a thin vertical strip of width dx is taken between the curves x=a and x=b. Hence, the height of this strip will be f(x) – g(x). So, the area of this strip dA is given as 

[ f(x) – g(x) ] dx.

Also, the total area is made up of a very large number of such strips, starting from x = a to x = b. Therefore, the total area A, between the curves is given by adding the area of all such strips between a and b:

where f(x) ≥ g(x), in [a,b]

Case 2: Taking the case when two curves y=f(x) and y=g(x) are given, such that f(x) ≥ g(x) between x = a and x = c and f(x) ≤ g(x) between x = c  and x = b,

Highlights of the Area of Bounded Regions:

  • The area of the ellipse = π ∗ a ∗ b
  • The shift in the coordinate axis leads to the area enclosed by a curve to remain invariant.
  • To check the symmetry of the curve following steps are followed:
    • The curve is said to be symmetrical about the x-axis when y is changed to -y and there is no change in the curve.
    • The curve is said to be symmetrical about the y-axis when x is changed to -x and there is no change in the curve.
  • If there is no change in the area after interchanging x and y, it means that the curve is symmetric about the line y = x.

Discussion of Exercise Questions of RS Aggarwal Solutions for Class 12 Chapter 17 Area of Bounded Regions

  1. The exercise solutions of RS Aggarwal Class 12 Chapter 17 consist of a diverse set of functions, that is the area enclosed by parabolic curves or straight lines, and other sets of problems to help you in the comprehensive practice of the concepts in this chapter.
  2. In these exercise solutions, you will find an increasing level of difficulty as you will progress in your practice.
  3. This is a very crucial and scoring topic with substantial weightage in the question papers for the national level competitive engineering entrance exams.

Perks of RS Aggarwal Solutions for Class 12 Maths Chapter 17 by Instasolv

  1. The subject matter experts of Instasolv have prepared the RS Aggarwal Class 12 Solutions for Chapter 17 in line with CBSE board guidelines.
  2. At Instasolv, you will find answers to all the queries that may possibly arise while solving the problems.
  3. It is also an interactive platform, so you can rely completely on Instasolv platform.
  4. It is advised that you supplement your course textbook with these solutions of RS Aggarwal Maths book by Instasolv.
  5. The Instasolv experts make sure you return satisfied with the solutions, therefore you should unhesitatingly refer to Instasolv whenever you stumble upon a confusion.