🔴Definite Integration||CLASS 12||CBSE|BSEB|ICSE||For Board Exams|| With Best Concept||BY Sudeep Sir

Integration is the inverse process of differentiation. In the differential calculus, we are given a function and we have to find the derivative or differential of this function, but in the integral calculus, we are to find a function whose differential is given. Thus, integration is a process which is the inverse of differentiation. Then, ∫f(x) dx = F(x) + C, these integrals are called indefinite integrals or general integrals.where, C is an arbitrary constant by varying which one gets different anti-derivatives of the given function. Note: Derivative of a function is unique but a function can have infinite anti-derivatives or integrals.
Let f(x) be a function. Then, the collection of all its primitives is called the indefinite integral of f(x) and is denoted by ∫f(x)dx. Integration as inverse operation of differentiation. If d/dx {φ(x)) = f(x), ∫f(x)dx = φ(x) + C, where C is called the constant of integration or arbitrary.

#DefiniteIntegration #BySudeepSingh #CBSE12

Symbols f(x) → Integrand
f(x)dx → Element of integration
∫→ Sign of integral
φ(x) → Anti-derivative or primitive or integral of function f(x)
The process of finding functions whose derivative is given, is called anti-differentiation or integration.

# The topics covered under integrals 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

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 (∫).

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🔴 COORDINATE GEOMETRY:-
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🔴 DIFFERENTIATION(class12):-
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🔴 DETERMINANT (Class12)
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