Integration
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
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Integration
15 Lectures 00:53:48-
Integrals Syllabus
00:09:25 -
Overview of Integration
Preview00:05:08 -
Important Terms in Integration
Preview00:02:26 -
Formulas on Integration
Preview00:06:48 -
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
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Methods of Integration
13 Lectures 00:43:14-
Methods of Integration
Preview00:02:16 -
Method 1- Integration by Substitution
00:02:02 -
∫ tan x dx
00:02:38 -
∫ cot x dx
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∫ 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
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Form ∫ P(x)dx/(ax + b)n
1 Lectures 00:04:33-
Problem on ∫ P(x)dx/(ax + b)n
00:04:33
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Form ∫ sin m x dx and ∫ cos m x dx
2 Lectures 00:07:21-
Problem on ∫ Sin4 x dx
Preview00:04:18 -
Problem on ∫ Cos4 x dx
00:03:03
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Form Product of Sin & / Or Cos
1 Lectures 00:05:38-
Evaluate ∫ Sin x Sin 2x Sin 3x dx
00:05:38
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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
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Form ∫ [f(x)]n f'(x) dx
1 Lectures 00:02:08-
Problem on ∫ [f(x)]n f'(x) dx
00:02:08
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Form ∫ (ax + b)n p(x) dx
1 Lectures 00:07:02-
Problem on ∫ (ax + b)n p(x) dx
00:07:02
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Form ∫ tanmx Sec2nx dx
1 Lectures 00:04:04-
Problem on ∫ tanmx Sec2nx dx
00:04:04
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Form ∫ Sinmx Cosnx dx
2 Lectures 00:11:03-
Problem 1 on ∫ Sinmx Cosnx dx
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Problem 2 on ∫ Sinmx Cosnx dx
00:05:13
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Trigonometric Substitution
2 Lectures 00:06:53-
Overview of Trigonometric Substitution
Preview00:01:40 -
Problem on Trigonometric Substitution
00:05:13
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Problems on Special Integrals
3 Lectures 00:07:36-
Special Integrals Problem 1
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Special Integrals Problem 2
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Special Integrals Problem 3
00:02:54
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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
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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
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Form ∫ px + q dx / ax2 + bx + c
1 Lectures 00:07:04-
Problem on Form ∫ px + q dx / ax2 + bx + c
00:07:04
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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
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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
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Integration by Parts
4 Lectures 00:10:10-
Overview of Integration by Parts
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Integration by Parts Problem 1
Preview00:02:47 -
Integration by Parts Problem 2
00:05:14 -
Integration by Parts Problem 3
00:01:19
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Form ∫ [ex {f(x) + f'(x)}] dx
3 Lectures 00:09:59-
Overview of ∫ [ex {f(x) + f'(x)}] dx
00:01:37 -
Problem 1 on ∫ [ex {f(x) + f'(x)}] dx
00:04:36 -
Problem 2 on ∫ [ex {f(x) + f'(x)}] dx
00:03:46
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Form ∫ eax sin bx dx
2 Lectures 00:06:28-
Overview of ∫ eax sin bx dx
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Problem on ∫ eax sin bx dx
00:04:45
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Form ∫ eax cos bx dx
2 Lectures 00:05:29-
Overview of ∫ eax cos bx dx
00:01:43 -
Problem on ∫ eax cos bx dx
00:03:46
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Form ∫ √a2 - x2 dx
2 Lectures 00:02:53-
Overview of ∫ √a2 - x2 dx
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Problem on ∫ √a2 - x2 dx
00:01:41
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Form ∫ √x2 - a2 dx
2 Lectures 00:02:36-
Overview of ∫ √x2 - a2 dx
Preview00:00:59 -
Problem on ∫ √x2 - a2 dx
00:01:37
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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
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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
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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
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Integration by Partial Fractions
6 Lectures 00:31:38-
What is Partial Fractions?
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Integration by Partial Fractions Overview
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Partial Fractions Problem 1
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Partial Fractions Problem 2
00:06:06 -
Partial Fractions Problem 3
00:06:31 -
Partial Fractions Problem 4
00:03:46
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Definite Integration
5 Lectures 00:18:46-
Overview of Definite Integration
Preview00:03:02 -
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
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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
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Properties of Definite Integral Problem Example 4
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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
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Limit of Sum
4 Lectures 00:21:32-
Overview of Limit of Sum
00:06:30 -
Formulas Used in Limit of Sum
Preview00:03:12 -
Limit of Sum Problem Example 1
00:06:35 -
Limit of Sum Problem Example 2
00:05:15
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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
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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
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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.