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Area Under Curves

Area Calculation 


Area calculation is one of the most important chapters of Integral Calculus. It takes a real test of the skills of Integration and that too Definite Integral in particular. The chapters of Indefinite and Definite Integral are prerequisite to study the topic of Area Calculation in Integral calculus.

This chapter is devoted to the application of definite integration for calculating the area of the regions bounded by specified or derived curves. Comprehensive material is provided with the consideration of wide variety of regions. Efforts are made to present the subject matter in the most lucid manner in order to involve the students actively and intellectually. A large number of solved examples, both of objective type and subjective type, are so chosen as to cover all the possible variations of question likely to be encountered by the students in different competitive examinations. 

We have learnt that the definite integral between two values of Independent variable represents the area of the curve bound by the curve, the axis of the independent variable. Further, as we can calculate the area under one curve and the area under another curve then we can calculate the area between two curves. Depending upon the nature of the curves, this area can have different shapes and thus the tool of definite integral can be employed to calculate the area of different shapes. As a matter of fact, you will realize that the standard formulae to calculate the areas of different shapes can be derived by definite integral by choosing the appropriate curves. 

  1. Basic Concepts
  2. Working rule for finding the Area
  3. Area enclosed between the curves
  4. Solved Examples

Area Calculation is important from the perspective of scoring high in IIT JEE as there are few fixed pattern on which a number Multiple Choice Questions are framed on this topic. You are expected to do all the questions based on this to remain competitive in IIT JEE examination. It is very important to master these concepts as this this helps in many of the problems in Physics in your preparation for IIT JEE, AIEEE, DCE, EAMCET and other engineering entrance examinations.

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