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