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