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RD Sharma Class 12 Solutions Chapter 21 - Areas of Bounded Regions (Ex 21.4) Exercise 21.4

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Last updated date: 23rd May 2024
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Preparation with RD Sharma Class 12 Solutions Chapter 21

Free PDF Download of RD Sharma Class 12 Solutions Chapter 21 - Areas of Bounded Regions Exercise 21.4 solved by Expert Mathematics Teachers on Vedantu.com. All Chapter 21 - Areas of Bounded Regions Ex 21.4 Questions with Solutions for RD Sharma Class 12 Maths to help you revise the complete Syllabus and Score More marks. Register for online coaching for IIT JEE (Mains & Advanced) and other Engineering entrance exams.


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Competitive Exams after 12th Science

RD Sharma Class 12 Solutions Chapter 21 - Areas of Bounded Regions (Ex 21.4) Exercise 21.4

Introduction to Chapter

‘Areas of Bounded Region’ is Chapter 21 of RD Sharma Class 12 Maths which helps the students to learn about how to calculate the area of bounded regions. The very first step while calculating the area is identifying the region whose area is to be determined. Students also learn about the algorithm to find the area using horizontal and vertical stripes.

Students will talk about the application of integration in calculating the area of bounded regions. Integration is one of the most important parts of Maths. Therefore before beginning with the chapter ‘Areas of Bounded Region’, the integration concepts must be very clear to the student.


Sections of RD Sharma Maths Class 12 Chapter 21- Areas of Bounded Region

1. The area as a definite integral

 The area under, over, or below the curves can be found out using definite integrals. 

If a function is 

  • Positive- the area between the function and the s-axis is equal to the definite integral.

  • The negative- area will be -1 times the definite integral.

The area between two positive functions = Definite integral or higher function - Lower function

2. Area using Horizontal Stripes

Area bounded by x= g(y) and y-axis between line y=a, y=b can be given as

A = \[\int_{a}^{b} |x|.dy = \int_{a}^{b} |g(y)|.dy \]

3. Area using vertical stripes

Area bounded, if f(x) is continuous and non-negative function of x on the closed interval [a,b], between the x-axis and the vertical lines x=a and x=b can be given as

A = \[\int_{a}^{b} f(x)dx \]

4. Area between two curves

The formula for finding the area under two curves by using vertical elements

Area =  \[\int_{a}^{b} |y_{2} - y_{1}|dx\] 

Here \[y_{1}\] and \[y_{2}\] are functions of x

The formula for finding the area under the two curves by using horizontal elements

Area =  \[\int_{c}^{d} |x_{2} - x_{1}|dy\] 

Here \[x_{1}\] and \[x_{2}\] are functions of y


Exercise in RD Sharma Class 12 Maths Chapter 21- Areas of a Bounded Region

Exercise

Description

21.1

Questions regarding how to calculate the area bounded by the given curve, x-axis.

21.2

Questions regarding the calculation of area using horizontal stripes.

21.3

Questions regarding areas lying between two curves using vertical strips.

21.4

Questions regarding area lying between two curves using horizontal strips. 

FAQs on RD Sharma Class 12 Solutions Chapter 21 - Areas of Bounded Regions (Ex 21.4) Exercise 21.4

1. How to prepare for the Chapter Areas of a bounded region in Class 12?

Vedantu provides all the solutions to the problems discussed in the Class 12 Maths book for all Chapters. Everyone must be aware of the quote- “Practice makes a man Perfect”, similarly in Maths as well the practice is a must in order to gain perfection in the concepts. By practicing the questions the students get familiar with the concepts and methodology to solve problems in Board exams. All the integration concepts must be clear to the students in order to master the chapter 21 Areas of Bounded Region.


2. Is RD Sharma Maths book helpful in class 12 for Maths?

RD Sharma is one of the most preferred books for Class 12. It not only helps the students to understand the topic, but it also helps the students to grasp the concepts to their core. It has numerous questions in it which helps the students to practice and get perfection in solving the questions. If the students are also preparing for competitive exams after 12, there is no other book better than RD Sharma as it has questions that test the critical thinking skills of the students as well.

3. Why is the weightage of the Calculus Unit in Class 12 CBSE?

Calculus is the most important unit of Class 12 CBSE and it has the highest weightage with 44 marks out of 100. Therefore, it is very important for the students to prepare each and every Chapter in the unit which includes, Continuity and Differentiability, Applications of Derivatives, Integrals, Applications of the Integrals, and Differential Equations. If the students are aiming to score good marks in Class 12, then they should go for the Calculus Unit first and understand each and every concept clearly.