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RD Sharma Class 12 Chapter 21 Solutions (Area Bounded Regions)

RD Sharma Class 12 Maths Solutions Chapter 21 ‘Area Bounded Regions’ talks about the applications of Integration. As you will see in your graduate studies that Integration is one of the most significant applications in Science and Engineering, its use and concept must be understood in detail. This chapter of RD Sharma Solutions also utilises the concept of integration. The topics you’ll learn in Area Bounded Regions are Area as a Definite Integral, Area Using Vertical Strips, Area Using Horizontal Strips, Area between two curves by using vertical Strips, and Area between two curves by using Horizontal strips.

This book discusses the first application of Integration in calculating Area Bounded Regions in detail. This chapter comprises 4 exercises and a total of 84 questions. On practising these questions for a number of times, you’ll be familiar with the concept and the methodology to use its topics for implementing to solve problems in CBSE and competitive exams. 

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Topics in RD Sharma Class 12 Maths Solutions Chapter 21 Area Bounded Regions

Area as a Definite Integral

Let f(x) is a continuous function on a closed interval [a,b]. 

This means the area that curve bounds, y will be f(x).

This means the x-axis as well as the ordinate x = a, x=b are

Area Using Vertical Strips

Let the curve y = f(x) and bounds the area of a given region. The axis and the x = a, x = b are the ordinate, then we use the algorithm to find that

F(x) a continuous function that is defined on the closed interval [a,b] so that y, the curve is equal to f(x) is found above the x-axis on the closed interval [a, c]. Then, A, area of the region bounded by f(x), x-axis, x= b and x=a or y, the curve will be

Area using the Horizontal Strips

In order to find area of particular regions, it becomes important to form horizontal strips instead of vertical strips as we discussed earlier. Although the procedure of calculating the area using the horizontal strips is comparable to what we did use in vertical strips.

In order to calculate the area using the horizontal strips, we will denote the curve by x = f(y), y-axis, and the ordinates or lines are y=c, y = d.

Using the algorithm, we found that

Since, x = f(y), f(y) < 0 for c<y<e

x = f(y) > 0 for e<y<d

Area between two curves by using vertical strips

Here you’re going to learn about the area that lies between the two given curves lying one below the other curves. One curve may also lie on the left of the other curve. Say one curve is present below the other curve and we want to find the region’s area that is bounded by those curves by drawing vertical stripes right on their left and right then we can use the following formula.

Discussion of Exercises in RD Sharma Class 12 Maths Solutions for ‘Area Bounded Regions’

  1. The first exercise of the chapter 21 Area Bounded Regions discusses finding the area of the region bounded by the given curve, x-axis, and the two ordinates. There are 26 questions in total whose solutions give you an idea about how to calculate the area and get familiar with the concept.
  2. The second exercise of the Area Bounded Regions chapter 21 teaches you the methodology of calculating the area using the horizontal strips. In this methodology, you will consider the curve as x and consider the lines of y.
  3. The third exercise of RD Sharma Class 12 Solutions Maths Chapter 21 Area Bounded Regions talks about how you can solve areas lying between the two curves by using vertical strips.
  4. The fourth exercise of RD Sharma Area Bounded Regions teaches you to apply the formula and methodology of area bounded by the two curves by using horizontal strips.

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