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RD Sharma Class 12 Maths Solutions Chapter 21 - Areas of Bounded Regions

Last updated date: 17th Apr 2024
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Chapter 21 - Areas of Bounded Regions - Free PDF Download

Mathematics is an important subject of Class 12 that can help you to score high marks and increase your percentage to the next level. Though a lot of students find it difficult to understand this subject at its core. But if you do, you can magically increase your score to higher than ever. So here, at Vedantu, we provide you with all the study material you will ever need to make Maths easier, fun, and scoring. 

About the Chapter Areas of Bounded Regions

  1. A function defined on a region of the complex plane is of the bounded form if it is equal to the ratio of two bounded analytical functions in that region.

  2. Most of the areas of bounded regions problems are application-oriented problems of calculus, especially integration. 

And so it is important for students to understand the concepts and learn carefully by using RD Sharma Class 12 Chapter 21 Solutions to score good marks in their exams. The solutions to important questions are explained in a step-by-step manner so that all the doubts of students are getting clarified when referring through RD Sharma solutions. Students can find a free PDF version of RD Sharma Class 12 Chapter 21 Solutions which is available on the Vedantu platform.

Competitive Exams after 12th Science

Benefits of Practicing Chapter Areas of Bounded Regions from R.D. Sharma for the Students of Class 12

CBSE and all the other boards have always considered RD Sharma as an important reference especially for students of Class 12. As a result, a lot of questions from RD Sharma have found their places in the set of Final Question papers of the Board exam. Some of the key points that make RD Sharma most reliable and helpful for students are as follows-

  • RD Sharma helps students to inculcate prompt decision making, pressure handling, and finding out the best possible solution at the time.

  • RD Sharma holds credibility among students, experienced academic demeanor in this subject, and over the years has developed its importance evermore.

  • RD Sharma helps students to familiarize themselves with all kinds of questions and math problems. From basics to advanced level, this reference book is a pitcher of its kind.

  • RD Sharma provides value to the students in search of excellence. And in pursuit of perfection, who knows when you land on one of the questions from your final paper of board exam! 

  • RD Sharma will make students push their boundaries and comfort levels to perform better and better every time. As they say, the best competition is always with the self.


Merits Of Learning And Practising Maths From Vedantu!

  1. Vedantu is an online educational platform that focuses on learning beyond excellence. We provide you with all the necessary material that students of Class 12 will require to study for their exams.

  2. From revision notes to CBSE sample question papers, from NCERT Solutions to previous year's question papers Vedantu has it all. And as provided here, RD Sharma solutions for those students who crave perfection and aim to achieve high marks in Class 12 mathematics.

  3. Vedantu provides step-by-step quality solutions of all Chapters solved by experts in the field for students of all Classes from 7 to 12.

  4. Interested students can also register and apply for IIT and JEE examinations and other competitive engineering exams at

Therefore, for all the students of Class 12 who are in pursuit of excellence and aim to score high marks and set a record in the examination, this is for you. The solved exercises of the Chapter Areas of bounded regions fall under the category of Calculus, the unit of highest weightage in the exam. So what are you waiting for? Download free PDF of Chapter Areas of Bounded regions of RD Sharma with solutions solved by experts in mathematics.

FAQs on RD Sharma Class 12 Maths Solutions Chapter 21 - Areas of Bounded Regions

1. How to determine the Areas of Bounded Regions?

The area of a bounded region can be determined directly by evaluating a definite integral of a graph of a function, the x‐axis, and two vertical boundaries.

2. How important is the Area of bounded regions for class 12 students?

In order to measure regions of different geometrical figures, including triangles, rectangles, trapezia and circles, we have studied formulas. The elementary geometry formulae allow us to calculate the areas of several simple figures. They are, however, insufficient for the measurement of the areas enclosed by curves. We have to analyze the field of bounded regions using certain Integral Calculus definitions for that.

3. Where can I find the RD Sharma Class 12 Areas of Bounded Regions Solutions?

Students can find a free PDF of RD Sharma Class 12 Chapter 21 Solutions from the Vedantu platform which are developed according to the NCERT curriculum.

4. How long will it take for students of Class 12 to solve all the exercises of Chapter Areas of bounded regions of RD Sharma?

The Chapter Areas of bounded regions of Class 12 consists of 5 exercises in total in RD Sharma. Each exercise has 29, 5, 51, 4, and 33 questions in order. So it will take a minimum of 7 to 8 hours for students to solve all the questions. Therefore, It is advisable to complete this Chapter in parts.

5. Why is it so important to cover the Chapter Area of bounded regions when the syllabus is so vast with lots of questions?

The Chapter Area of Bounded regions is indeed a big Chapter to complete. But the truth is that in the marking scheme, this Chapter is a part of the topic Calculus, which holds a weightage of 35 marks in the exam. So instead of considering this as a time-consuming Chapter, students can consider it as a bonus of scoring high marks. Also, to make your learning fun visit Vedantu to download all the keynotes to revise and start solving the exercise. 

6. How to prepare for the Chapter Area of Bounded Regions if I am weak at Maths?

First things first, solve NCERT questions to understand and cover the basics of the Chapter Area of Bounded Regions. Once completed, then shift your focus to the key notes and revision notes available at to brush up on all that is required. After that, try to solve RD Sharma and understand the depth of each question. Lastly, solve previous year’s questions on this topic to gain confidence. Check your mistakes and track your progress. And voila, you made it!