RD Sharma Class 12 Solutions Chapter 21 - Areas of Bounded Regions (Ex 21.3) Exercise 21.3

• RD Sharma is an author of several textbooks, a well-known Mathematician and an educator. 

• RD Sharma's books are very popular among students of the CBSE board. RD Sharma’s books for Mathematics are considered to be one of the best and most important books in mathematics for Classes 9 to 12. These books are a complete package that includes a complete syllabus and relevant questions to practice from. 

• There are a lot of Maths topics covered in RD Sharma Solutions for Class 12 Maths book, some of them are quadratic equations, coordinate geometry, heights and distances, triangles, circles, trigonometric ratios, trigonometric identities, probability, pairs of linear equations in two variables, surface, area and volumes, arithmetic progressions, and many more. 

• Class 12 is considered to be an important phase in a student's life as a lot of academic decisions are made during this time for which good educational resources are needed to gain knowledge. It is important that students should study from limited and good resources and RD Sharma’s book is one of them.

• These books contain everything which a student wants. These books have a lot of exercises in each chapter and each exercise contains an ample amount of questions to practise which helps students in having good knowledge. 

Benefits of RD Sharma Class 12 Solutions for Maths

This book has given us every reason to opt for this book. This book has its own value in front of students and teachers. This book has explained each and every concept in a detailed manner which enables the students to go for this book. Students can easily learn the concepts and can score good marks in their examinations. Even those students who are weaker in their studies can easily understand the concepts and gain good marks. Along with this, a lot of questions are also there in the book which makes it easy for the students to practice on their own. This book is written by a renowned author RD Sharma, which strikes out the doubt of non-authenticity. A student can definitely go for this book. This book provides you with a complete package for knowledge-based books which is exam oriented also. This book by RD Sharma is considered to be one of the important books which are very helpful for students. 

The Topics Covered in Chapter 21 – Areas of Bounded Regions

In this chapter, you will understand how to find areas of different geometrical figures plotted on the coordinate axes. 

Definition of the area of a figure: Area of a geometrical figure (also known as an equation) is generally defined as the area enclosed between the figure and the x-axis. By convention, the area which is above the x-axis (i.e., for the positive y-axis) is taken as positive and the area which is below the x-axis (i.e., for the negative y-axis) is taken as negative. To calculate the total area (in a given range), each area is taken with a sign. If the modulus of the area is asked, then add all positive areas and add the modulus of the sum of all negative areas. 

Important  Points to Keep in Mind for This Chapter

• Always keep in mind the domain given in the question for which area is asked.

For example: Find the area of y=x  for 

1. x from 2 to 4

2. x from 2 to 6

For the first section, the answer is 6 and for the second section, the answer is 16. So, this illustrates the importance of domain while finding areas of figures in coordinate axes.

• Be careful of the sign of the area. If you are breaking the figure into different parts and then finding the area, don't forget to take each area with its proper sign.