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L-1 - Indefinite Integration

This document provides information about indefinite integration or antidifferentiation. It discusses key concepts such as the constant of integration, standard formulas using definitions and theorems of integration, and the substitution method of integration. Examples of standard integrals are provided for practice, as well as problems evaluating definite integrals using the substitution method. Information is also given on live JEE preparation classes on Unacademy covering physics, mathematics, and chemistry for JEE 2023, 2024 aspirants.

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MOKSH AGARWAL
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568 views92 pages

L-1 - Indefinite Integration

This document provides information about indefinite integration or antidifferentiation. It discusses key concepts such as the constant of integration, standard formulas using definitions and theorems of integration, and the substitution method of integration. Examples of standard integrals are provided for practice, as well as problems evaluating definite integrals using the substitution method. Information is also given on live JEE preparation classes on Unacademy covering physics, mathematics, and chemistry for JEE 2023, 2024 aspirants.

Uploaded by

MOKSH AGARWAL
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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12

CLASS

Indefinite
Integration
Standard Formulas &
Method of Substitution

SAMEER CHINCHOLIKAR
Sameer Chincholikar
IIT Roorkee
12+ Years of Teaching Experience
Trained Million+ students
Author - Top Ranker’s Series (TRS)
Bratin Mondal Amaiya Singhal

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Indefinite Integration:
Definition
Indefinite Integration : Definition

Integration is the reverse process of differentiation.


Indefinite Integration : Constant of Integration

The resulting function obtained by Indefinite Integration represents


a family of curves for which the slope at ‘x’ is constant.
Formula Set-1: Using Definition

1.
Formula Set-1: Using Definition

2.
Formula Set-1: Using Definition

3.

4.
Theorems of Integration

1.
Theorems of Integration

2.
Theorems of Integration

3.
Evaluate : (exlna -ealnx + 3ealna) dx
Evaluate :
Evaluate :
Evaluate :
Formula Set-1: Using Definition

5. 6.

7. 8.

9. 10.
Formula Set-1: Using Definition

11.
Formula Set-1: Using Definition

12.
Formula Set-1: Using Definition

13.
Formula Set-1: Using Definition

14.
Evaluate :
Evaluate :
2004
A. B.

C. D.
Evaluate:
Formula Set-1: Using Definition

15.

16.

17.
Evaluate :
Methods of
Integration
Methods of Integration

1. Substitution

2. By parts

3. Partial Fractions
Substitution Method
Concept Builder

Evaluate : ∫x2 sinx3 dx


Integration by substitution:

1.
Integration by substitution:

2.
dx is equal to

A. B.

C. D.
Evaluate :
Evaluate :
Evaluate :
Evaluate :
Substitution Method:
Practice Problems
Evaluate :

2004

A. (-cos 𝛂, sin 𝛂) B. (cos 𝛂, sin 𝛂)

C. (-sin 𝛂, cos 𝛂) D. (sin 𝛂, cos 𝛂)


A. B.

C. D.
A. B.

C. D.
A.

C.

B.

D.
A. -sin(sin2x + 1) + c B. cosec(sin 2x + 1)

C. -sec-1(sin2x + 1) + c D. tan-1(sin 2x + 1) + c
A. B.

C. D. None
Algebraic Formulas
Based on Substitution
Formula Set -2 : Based on Substitution

1.
Formula Set -2 : Based on Substitution

2.
Formula Set -2 : Based on Substitution

3.
Formula Set -2 : Based on Substitution

4.
Formula Set -2 : Based on Substitution

5.
Formula Set -2 : Based on Substitution

6.
then find the value of a and b

A. 1, -1 B. -1, 1 C. 1/2 , -1/2 D. 1/2 , 1/2


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