Integration

Simply Easy Learning

Created by Ridhi Arora, Last Updated 09-Aug-2019, Language:English

Description

Integration is one of the two main operations of calculus, with its inverse, differentiation, being the other.The principles of integration were formulated independently by Isaac Newton and Gottfried Leibniz.It can be used to find areas, volumes etc.We had already taken up differentiation.Hence this video series is based on Integrals for class 12 students for board level and IIT JEE Mains.

Audience

These video classes have been designed for Class 12 students (Non-medical students and commerce students with Mathematics), those who are preparing for CBSE and other Board Exams for Intermediate, +2 and IIT JEE entrance exams. These classes will also be helpful for students in preparing them for Competitive Examinations for Engineering Institutes like IIT JEE etc.

Course Content

Integration

15 Lectures 00:53:48
- Integrals Syllabus
  
  00:09:25
- Overview of Integration
  
  Preview
  
  00:05:08
- Important Terms in Integration
  
  Preview
  
  00:02:26
- Formulas on Integration
  
  Preview
  
  00:06:48
- Integration Problems Example
  
  00:02:35
- Geometric Interpretation of Integral
  
  00:02:41
- Properties of Indefinite Integrals
  
  00:01:50
- Integration Problem Example 1
  
  00:01:17
- Integration Problem Example 2
  
  00:03:18
- Integration Problem Example 3
  
  00:01:46
- Integration Problem Example 4
  
  00:03:00
- Integration Problem Example 5
  
  00:02:41
- Integration Problem Example 6
  
  00:05:14
- Integration Problem Example 7
  
  00:03:57
- Integration Problem Example 8
  
  00:01:42
Methods of Integration

13 Lectures 00:43:14
- Methods of Integration
  
  Preview
  
  00:02:16
- Method 1- Integration by Substitution
  
  00:02:02
- ∫ tan x dx
  
  00:02:38
- ∫ cot x dx
  
  00:02:25
- ∫ sec x dx
  
  00:02:45
- ∫ cosec x dx
  
  00:02:31
- ∫ (dx/x² - a²)
  
  00:04:41
- ∫ (dx/a² - x²)
  
  00:03:49
- ∫ (dx/√x² - a²)
  
  00:05:56
- ∫ (dx/√a² - x²)
  
  00:02:48
- ∫ (dx/√x² + a²)
  
  00:03:02
- ∫ (dx/√a² + x²)
  
  00:04:23
- Problems on Integrals
  
  00:03:58
Form ∫ P(x)dx/(ax + b)ⁿ

1 Lectures 00:04:33
- Problem on ∫ P(x)dx/(ax + b)ⁿ
  
  00:04:33
Form ∫ sin ^m x dx and ∫ cos ^m x dx

2 Lectures 00:07:21
- Problem on ∫ Sin⁴ x dx
  
  Preview
  
  00:04:18
- Problem on ∫ Cos⁴ x dx
  
  00:03:03
Form Product of Sin & / Or Cos

1 Lectures 00:05:38
- Evaluate ∫ Sin x Sin 2x Sin 3x dx
  
  00:05:38
Evaluation of Integrals

4 Lectures 00:12:58
- Integral of Sinx/Sin(x-a)
  
  00:02:30
- Evaluate ∫ Sin2x/a² Sin² x + b² Cos² x
  
  00:04:12
- Evaluate ∫ Tanx Tan2x Tan3x dx
  
  00:03:28
- Evaluate ∫ Tan⁴x dx
  
  00:02:48
Form ∫ [f(x)]ⁿ f^'(x) dx

1 Lectures 00:02:08
- Problem on ∫ [f(x)]ⁿ f^'(x) dx
  
  00:02:08
Form ∫ (ax + b)ⁿ p(x) dx

1 Lectures 00:07:02
- Problem on ∫ (ax + b)ⁿ p(x) dx
  
  00:07:02
Form ∫ tan^mx Sec²ⁿx dx

1 Lectures 00:04:04
- Problem on ∫ tan^mx Sec²ⁿx dx
  
  00:04:04
Form ∫ Sin^mx Cosⁿx dx

2 Lectures 00:11:03
- Problem 1 on ∫ Sin^mx Cosⁿx dx
  
  00:05:50
- Problem 2 on ∫ Sin^mx Cosⁿx dx
  
  00:05:13
Trigonometric Substitution

2 Lectures 00:06:53
- Overview of Trigonometric Substitution
  
  Preview
  
  00:01:40
- Problem on Trigonometric Substitution
  
  00:05:13
Problems on Special Integrals

3 Lectures 00:07:36
- Special Integrals Problem 1
  
  00:02:16
- Special Integrals Problem 2
  
  00:02:26
- Special Integrals Problem 3
  
  00:02:54
Form ∫ dx/ ax² + bx + c

2 Lectures 00:07:57
- Problem 1 on ∫ dx/ ax² + bx + c
  
  00:03:38
- Problem 2 on ∫ dx/ ax² + bx + c
  
  00:04:19
Form ∫ (dx/√ax² + bx + c

2 Lectures 00:06:08
- Problem 1 on ∫ (dx/√ax² + bx + c
  
  00:02:41
- Problem 2 on ∫ (dx/√ax² + bx + c
  
  00:03:27
Form ∫ px + q dx / ax² + bx + c

1 Lectures 00:07:04
- Problem on Form ∫ px + q dx / ax² + bx + c
  
  00:07:04
Form ∫ dx / a sin ² x + b cos ² x

1 Lectures 00:03:51
- Problem on ∫ dx / a sin ² x + b cos ² x
  
  00:03:51
Form ∫ dx / a sin x + b cos x

1 Lectures 00:04:39
- Problem on ∫ dx / a sin x + b cos x
  
  00:04:39
Integration by Parts

4 Lectures 00:10:10
- Overview of Integration by Parts
  
  00:00:50
- Integration by Parts Problem 1
  
  Preview
  
  00:02:47
- Integration by Parts Problem 2
  
  00:05:14
- Integration by Parts Problem 3
  
  00:01:19
Form ∫ [e^x {f(x) + f'(x)}] dx

3 Lectures 00:09:59
- Overview of ∫ [e^x {f(x) + f'(x)}] dx
  
  00:01:37
- Problem 1 on ∫ [e^x {f(x) + f'(x)}] dx
  
  00:04:36
- Problem 2 on ∫ [e^x {f(x) + f'(x)}] dx
  
  00:03:46
Form ∫ e^ax sin bx dx

2 Lectures 00:06:28
- Overview of ∫ e^ax sin bx dx
  
  00:01:43
- Problem on ∫ e^ax sin bx dx
  
  00:04:45
Form ∫ e^ax cos bx dx

2 Lectures 00:05:29
- Overview of ∫ e^ax cos bx dx
  
  00:01:43
- Problem on ∫ e^ax cos bx dx
  
  00:03:46
Form ∫ √a² - x² dx

2 Lectures 00:02:53
- Overview of ∫ √a² - x² dx
  
  00:01:12
- Problem on ∫ √a² - x² dx
  
  00:01:41
Form ∫ √x² - a² dx

2 Lectures 00:02:36
- Overview of ∫ √x² - a² dx
  
  Preview
  
  00:00:59
- Problem on ∫ √x² - a² dx
  
  00:01:37
Form ∫ √x² + a² dx

2 Lectures 00:02:30
- Overview of ∫ √x² + a² dx
  
  00:01:10
- Problem on ∫ √x² + a² dx
  
  00:01:20
Form ∫ √ax² + bx + c dx

2 Lectures 00:03:44
- Overview of ∫ √ax² + bx + c dx
  
  00:01:13
- Problem on ∫ √ax² + bx + c dx
  
  00:02:31
Form ∫ px + q √ax² + bx + c dx

2 Lectures 00:08:03
- Overview of ∫ (px + q) √ax² + bx + c dx
  
  00:02:08
- Problem on ∫ (px + q) √ax² + bx + c dx
  
  00:05:55
Integration by Partial Fractions

6 Lectures 00:31:38
- What is Partial Fractions?
  
  00:02:32
- Integration by Partial Fractions Overview
  
  00:04:14
- Partial Fractions Problem 1
  
  00:08:29
- Partial Fractions Problem 2
  
  00:06:06
- Partial Fractions Problem 3
  
  00:06:31
- Partial Fractions Problem 4
  
  00:03:46
Definite Integration

5 Lectures 00:18:46
- Overview of Definite Integration
  
  Preview
  
  00:03:02
- Definite Integration Problem Example 1
  
  00:03:52
- Definite Integration Problem Example 2
  
  00:05:06
- Definite Integration Problem Example 3
  
  00:02:42
- Definite Integration Problem Example 4
  
  00:04:04
Properties of Definite Integral

9 Lectures 00:45:44
- Overview of Properties of Definite Integral
  
  00:02:49
- Advanced Properties of Definite Integral
  
  00:04:47
- Properties of Definite Integral Problem Example 1
  
  00:06:32
- Properties of Definite Integral Problem Example 2
  
  00:03:57
- Properties of Definite Integral Problem Example 3
  
  00:03:57
- Properties of Definite Integral Problem Example 4
  
  00:05:05
- Properties of Definite Integral Problem Example 5
  
  00:05:17
- Properties of Definite Integral Problem Example 6
  
  00:06:23
- Properties of Definite Integral Problem Example 7
  
  00:06:57
Limit of Sum

4 Lectures 00:21:32
- Overview of Limit of Sum
  
  00:06:30
- Formulas Used in Limit of Sum
  
  Preview
  
  00:03:12
- Limit of Sum Problem Example 1
  
  00:06:35
- Limit of Sum Problem Example 2
  
  00:05:15
Miscellaneous Problems Integrals

4 Lectures 00:22:28
- Integrals Miscellaneous Problem Example 1
  
  00:07:12
- Integrals Miscellaneous Problem Example 2
  
  00:03:35
- Integrals Miscellaneous Problem Example 3
  
  00:06:55
- Integrals Miscellaneous Problem Example 4
  
  00:04:46
IIT JEE Questions on Integrals

4 Lectures 00:21:38
- Integrals IIT JEE Problem Example 1
  
  00:04:24
- Integrals IIT JEE Problem Example 2
  
  00:06:36
- Integrals IIT JEE Problem Example 3
  
  00:04:13
- Integrals IIT JEE Problem Example 4
  
  00:06:25

Ridhi Arora

Ridhi Arora holds a B. Tech Honors - Gold medalist in Computer Science. Ridhi is an ardent learner, a keen observer and a passionate Mathematics faculty for classes 11,12 and IIT JEE Mains. She is among the top 10 most viewed writers in Kota, Rajasthan, on Quora. Ridhi is also associated with Ganit Hub as Algebra HOD and Miracle Live Coaching Private Limited as a Mathematics faculty. Ridhi is a confident and dynamic trainer with a total teaching experience of 5+ years.