Integrals

Level STD 12 CBSE | Maths

Topic Tree

I. Indefinite Integrals

1. Integration of Simple Algebraic Functions and Simple Exponential Functions
2. Integration of Simple Trigonometric Functions
3. Integration by Substitution
4. Integration of Odd & Even Powers of sin x, cos x and tan x
5. Integration Using Standard Formulae
6. Directly using Formulae & Special Types of Integrals

7. Integration Using Partial Fractions
8. Integration By Parts
9. Repeating After Twice Integration
10. Integrals of Exponential Forms
11. Three More Formulae for Integration
12. Integration of Special functions

II. Definite Integrals

13. Formula for limit of a sum
14. Direct Evaluation of Definite Integrals
15. Properties of Definite Integrals
16. Integration of Modulus of a Function
17. Odd and Even Functions

Introduction

Concept maps and flashcards

1. Partial fraction techniques in integrals
2. Integrals flash cards
3. Integrals Formulae

NOTES

Integrals – an introduction

Antiderivative by method of inspection

Quiz in Antiderivatives – Activity

Antiderivatives – worksheet-1 | worksheet-2

Basic formula of Integrals

Substitution Methods – Worksheet-1 | Worksheet-2 | Worksheet-3

Integral by parts

Partial Fractions Decomposition

Unit Test-1

Sketch note summary and Mnemonics

Question Bank

1. Integrals one mark questions | Key
2. Integrals by substitution questions | Key
3. Unit test | Set-1 | Key-1 | Set-2 | Key-2 | Set-3 | Key-3 | Set-4 | Key-4 | Set-5 | Key-5

Video

1. Integrals part 1
2. Integrals part 2
3. Integral of sin x . sin(cos x)dx solved by Gokul
4. Doubt clinic session on integrals
5. Definite integral part 1
6. Integral by parts by Bernoullis formula demonstrated by Pavani, Hari and Dhanusri
7. Integral problem using partial fraction
8. Integral problem with trigonometry formula and substitution method a tutorial session with shreya
9. Definite integral as limit of sum example problem 2
10. Definite integral as limit of sum theory part 1
11. Definite integral as a limit of sum
12. Definite integral as limit of sum theory part 2
13. Definite integral as limit of sum theory part 3
14. Definite integral as limit of sum theory part 4
15. Integral between the limits 0 and pi of x . (sin^2(sin x) + cos^2(cos x) dx presented by Shravanth
16. Recitation of some trigonometric formulae used in integrals
17. Integration demo

PPT Notes

1. Integrals of trigonometric functions

Additional Notes

1. Integral doubt question 1
2. Integral doubt question 2
3. Integral doubt question 3