Integrals For Class 12

Integrals class 12, chapter 7 deals with the study of definite and indefinite integrals and their elementary properties. The development of integral calculus arises out to solve the problems of the following types:

  • The problem of finding the function whenever the derivatives are given
  • The problem of finding the area bounded by the graph function under certain conditions.

These two problems lead to the development of integral calculus (definite integral and indefinite integral)

Integrals Class 12 Concepts

The topics and subtopics covered under integrals class 12 Maths are:

  • Introduction
  • Integration as an inverse process of differentiation
  • Geometrical interpretation of indefinite integral
  • Some properties of indefinite integrals
  • Comparison between differentiation and integration
  • Methods of integration
  • Integration by substitution
  • Integration using trigonometric identities
  • Integrals for some particular functions
  • Integration by partial fractions
  • Integration by parts
  • Integral of the type
  • Integrals for some more types
  • Definite integral
  • Definite integral as a limit of a sum
  • The fundamental theorem of calculus
  • Area function
  • The first fundamental theorem of integral calculus
  • The second fundamental theorem of integral calculus
  • Evaluation 0f definite integrals by substitution
  • Some properties of definite integrals

Integrals Class 12 Notes

We are already aware that if a function f(x) is differentiable on an interval I, then it’s derivative f’(x) exist at each point of I. Now the question arises if the derivative of the function is known to us, is it possible to obtain the function. The answer to this question is yes. By the means of Integration ( or antiderivative of a function), it is possible to obtain the original function.

Integral Types

The integral calculus is of the two forms, namely

(i) Indefinite Integral

(ii) Definite Integral

In an indefinite integral, the range of the function is not defined, thus the value of the function obtain is followed by a constant value ‘c.’

Whereas in a definite integral, the range of the function is well defined, thus it gives a well-defined function.

The integration is denoted by \((\int)\).

Antiderivative Functions

Let us have a look at various antiderivative of functions.

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