- published: 01 May 2016
- views: 518675
Integration may refer to:
In calculus, the power rule is used to differentiate functions of the form , whenever
is a real number. Since differentiation is a linear operation on the space of differentiable functions, polynomials can also be differentiated using this rule.
If is a function such that
, and
is differentiable at
, then,
The power rule for integration, which states that
for any real number , may be derived by applying the Fundamental Theorem of Calculus to the power rule for differentiation.
To start, we should choose a working definition of the value of , where
is any real number. Although it is feasible to define the value as the limit of a sequence of rational powers that approach the irrational power whenever we encounter such a power, or as the least upper bound of a set of rational powers less than the given power, this type of definition is not amenable to differentiation. It is therefore preferable to use a functional definition, which is usually taken to be
for all values of
, where
is the natural exponential function and
is Euler's number. First, we may demonstrate that the derivative of
is
.
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MIT grad shows how to find antiderivatives, or indefinite integrals, using basic integration rules. More videos with Nancy coming in 2017! To skip ahead: 1) For how to integrate a polynomial with the POWER RULE, skip to 1:35. 2) For how to integrate NEGATIVE POWERS of x, FRACTIONAL POWERS of x, and RADICALS/ROOTS, skip to 6:12. 3) For how to integrate x^(-1), or 1/x, with the LOG RULE, skip to 7:23. 4) For examples where you use more algebra to rewrite before integrating, to SEPARATE the numerator of a FRACTION, or EXPAND a PRODUCT in order to use the Power Rule, skip to 10:00. 5) For basic TRIG and EXPONENTIAL examples that use rules from the Table of Integrals, as well as trig identities, skip to 11:36. For my video on how to integrate using U-SUBSTITUTION, jump to: https://youtu.be/kTX...
Lots of Basic Antiderivative / Integration Examples
In this video I introduce the concept of an integral for the first time. I feel that in school etc., people are not told what an integral IS but rather how to compute an integral. I think that is the wrong way to go about doing business, so here i go, enjoy!! Visit www.universityphysicstutorials.com Follow me on Twitter @adambeatty503 Follow me on Facebook @UniversityPhysicsTutorials
SAME VIDEO WITH IMPROVED AUDIO 👇👇👇👇👇👇👇 LINK : https://youtu.be/_uP1MZlqQBI .............................................................................................................. This video will explain how to learn the integration formulas of some special functions. ENJOY WATCHING!!! ..................................................................................................... My name is Gaurav and i have a mission of making studies easy for the students. So for that it is really very important for me to help the students to learn the difficult formulas and concepts of physics, maths and chemistry. So to support me in this mission all you need to do is to share these videos as much as you can with your friends and teachers This is a must watch video for all maths aspir...
► Get your FREE Applications of Integrals formula sheet: http://learn.kristakingmath.com/applications-of-integrals/ ► Subscribe to my channel // http://www.youtube.com/subscription_center?add_user=TheIntegralCalc In this calculus overview video you'll learn about four very common applications of integration: average value, area between curves, arc length and surface area of revolution. These applications of integration are the four most commonly taught, but they're also the most abstract. I'll show you what it really means to find the average value of a function, explain how to find the area between two curves, show you what arc length is really representing, and describe how surface area of revolution is really just an application of arc length. We'll also talk about how each of these...
MIT grad shows how to integrate by parts and the LIATE trick. More videos with Nancy coming in 2017! To skip ahead: 1) For how to use integration by parts and a good RULE OF THUMB for CHOOSING U and DV, skip to time 2:46. 2) For the TRICK FOR CHOOSING U and DV (the LIATE memory trick) skip to 10:12. WHEN to use INTEGRATION BY PARTS: If you have an integral to evaluate, and you don't already know how to integrate it, as is, then see if you can simplify it somehow with algebra. If not, try doing a substitution, like U-Substitution. If U-Substitution does not help, then you may need to use the INTEGRATION BY PARTS formula. RULE OF THUMB: The first step to use Integration by Parts is to pick your "u" and "dv". As a general rule of thumb, whichever factor in your integrand gets simpler when y...
MIT grad shows how to do integration using u-substitution (Calculus). More videos with Nancy coming in 2017! To skip ahead: 1) for a BASIC example where your du gives you exactly the expression you need in order to substitute, skip to time 1:30. 2) For an example where you have to REARRANGE THE DU by multiplying or dividing because the du has a different number or sign than what you need, skip to time 8:21. 3) For one where you have to REARRANGE THE U by subtracting or adding because the du expression cannot give you the expression you need, skip to 17:15. 4) For u-substitution with TRIG (SIN/COS) and the power rule, skip to 22:35. With all u-substitution integration problems: The FIRST STEP is to pick your "u". The best choice is usually the longer x-expression that is inside a power or...
MIT grad shows how to find antiderivatives, or indefinite integrals, using basic integration rules. More videos with Nancy coming in 2017! To skip ahead: 1) For how to integrate a polynomial with the POWER RULE, skip to 1:35. 2) For how to integrate NEGATIVE POWERS of x, FRACTIONAL POWERS of x, and RADICALS/ROOTS, skip to 6:12. 3) For how to integrate x^(-1), or 1/x, with the LOG RULE, skip to 7:23. 4) For examples where you use more algebra to rewrite before integrating, to SEPARATE the numerator of a FRACTION, or EXPAND a PRODUCT in order to use the Power Rule, skip to 10:00. 5) For basic TRIG and EXPONENTIAL examples that use rules from the Table of Integrals, as well as trig identities, skip to 11:36. For my video on how to integrate using U-SUBSTITUTION, jump to: https://youtu.be/kTX...
Lots of Basic Antiderivative / Integration Examples
In this video I introduce the concept of an integral for the first time. I feel that in school etc., people are not told what an integral IS but rather how to compute an integral. I think that is the wrong way to go about doing business, so here i go, enjoy!! Visit www.universityphysicstutorials.com Follow me on Twitter @adambeatty503 Follow me on Facebook @UniversityPhysicsTutorials
SAME VIDEO WITH IMPROVED AUDIO 👇👇👇👇👇👇👇 LINK : https://youtu.be/_uP1MZlqQBI .............................................................................................................. This video will explain how to learn the integration formulas of some special functions. ENJOY WATCHING!!! ..................................................................................................... My name is Gaurav and i have a mission of making studies easy for the students. So for that it is really very important for me to help the students to learn the difficult formulas and concepts of physics, maths and chemistry. So to support me in this mission all you need to do is to share these videos as much as you can with your friends and teachers This is a must watch video for all maths aspir...
► Get your FREE Applications of Integrals formula sheet: http://learn.kristakingmath.com/applications-of-integrals/ ► Subscribe to my channel // http://www.youtube.com/subscription_center?add_user=TheIntegralCalc In this calculus overview video you'll learn about four very common applications of integration: average value, area between curves, arc length and surface area of revolution. These applications of integration are the four most commonly taught, but they're also the most abstract. I'll show you what it really means to find the average value of a function, explain how to find the area between two curves, show you what arc length is really representing, and describe how surface area of revolution is really just an application of arc length. We'll also talk about how each of these...
MIT grad shows how to integrate by parts and the LIATE trick. More videos with Nancy coming in 2017! To skip ahead: 1) For how to use integration by parts and a good RULE OF THUMB for CHOOSING U and DV, skip to time 2:46. 2) For the TRICK FOR CHOOSING U and DV (the LIATE memory trick) skip to 10:12. WHEN to use INTEGRATION BY PARTS: If you have an integral to evaluate, and you don't already know how to integrate it, as is, then see if you can simplify it somehow with algebra. If not, try doing a substitution, like U-Substitution. If U-Substitution does not help, then you may need to use the INTEGRATION BY PARTS formula. RULE OF THUMB: The first step to use Integration by Parts is to pick your "u" and "dv". As a general rule of thumb, whichever factor in your integrand gets simpler when y...
MIT grad shows how to do integration using u-substitution (Calculus). More videos with Nancy coming in 2017! To skip ahead: 1) for a BASIC example where your du gives you exactly the expression you need in order to substitute, skip to time 1:30. 2) For an example where you have to REARRANGE THE DU by multiplying or dividing because the du has a different number or sign than what you need, skip to time 8:21. 3) For one where you have to REARRANGE THE U by subtracting or adding because the du expression cannot give you the expression you need, skip to 17:15. 4) For u-substitution with TRIG (SIN/COS) and the power rule, skip to 22:35. With all u-substitution integration problems: The FIRST STEP is to pick your "u". The best choice is usually the longer x-expression that is inside a power or...
Lots of Basic Antiderivative / Integration Examples
MIT grad shows how to do integration using u-substitution (Calculus). More videos with Nancy coming in 2017! To skip ahead: 1) for a BASIC example where your du gives you exactly the expression you need in order to substitute, skip to time 1:30. 2) For an example where you have to REARRANGE THE DU by multiplying or dividing because the du has a different number or sign than what you need, skip to time 8:21. 3) For one where you have to REARRANGE THE U by subtracting or adding because the du expression cannot give you the expression you need, skip to 17:15. 4) For u-substitution with TRIG (SIN/COS) and the power rule, skip to 22:35. With all u-substitution integration problems: The FIRST STEP is to pick your "u". The best choice is usually the longer x-expression that is inside a power or...
What is an integral? How do you think about it? Check out the Art of Problem Solving: https://aops.com/3blue1brown Full playlist: http://3b1b.co/calculus Support for these videos comes primarily from Patreon: https://patreon.com/3blue1brown Special thanks to the following patrons: http://3b1b.co/eoc8-thanks ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3Blue...
This calculus video tutorial explains how to find the indefinite integral of function. It explains how to apply basic integration rules and formulas to help you integrate functions. This video contains plenty of examples and practice problems. Calculus Video Playlist: https://www.youtube.com/watch?v=rCxi-O79sVo&t;=25s&index;=1&list;=PL0o_zxa4K1BVKErFko9je9IBZ0hXWXVtV Access to Premium Videos: https://www.patreon.com/MathScienceTutor Here is a list of topics: 1. Basic Integration Rules and Formulas 2. Indefinite Integral and Constant of Integration 3. Integrating Constants and Linear Functions 4. Parabolic and Quadratic Functions 5. Polynomial Functions 6. Integration of Rational Functions and Fractions 7. Indefinite Integral - Square Root and Radical Functions 8. Exponential Funct...
o Exam : JEE Main + Advanced o Course Type : IIT JEE Online Coaching Video Lectures (DVD, VOD) o Course Name : Simplified Mathematics Vol. 4: Calculus-Indefinite & Definite Integration by MC sir o Class : 12th, 13th (12th pass) o Medium : English o Course Code : 930 o http://www.etoosindia.com/simplified-mathematics-vol-4-calculus-indefinite-definite-integration MC Sir is known for his focused and simplified JEE teaching to bring to students an easy and analytical methodology towards IIT JEE. The main focus of this course is to develop solid foundation concept and fundamentals. This course designed and developed by the experienced faculty of KOTA and www.etoosindia.com 's staff. http://www.etoosindia.com The Best Performance JEE Online Coaching for JEE Main, Advanced & CBSE | An...
Examples of not so easy integration using the Basic Integration Rules at 2:57 7:44 11:22 19:08 22:38 34:16 I would like to send out a HUGE THANK YOU to my YouTube student Jigyasa Nigam that did the Closed Captioning of this lesson for me. Your support and help is greatly appreciated:D Check out http://www.ProfRobBob.com, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com
in this video you can watch how the integration evolved step by step.
UCI Math 2B: Single-Variable Calculus (Fall 2013) Lec 14. Single-Variable Calculus -- Strategy for Integration -- View the complete course: http://ocw.uci.edu/courses/math_2b_calculus.html Instructor: Natalia L. Komarova Ph.D. License: Creative Commons CC-BY-SA Terms of Use: http://ocw.uci.edu/info More courses at http://ocw.uci.edu Description: UCI Math 2B is the second quarter of Single-Variable Calculus and covers the following topics: Definite integrals; the fundamental theorem of calculus. Applications of integration including finding areas and volumes. Techniques of integration. Infinite sequences and series. Parametric and polar equations. Recorded on October 30, 2013 Required attribution: Komarova, Natalia L. Math 2B (UCI OpenCourseWare: University of California, Irvine), http:...
Calculus 2 Lecture 7.1: Integration By Parts
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Go with me down
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[Chorus]
(Eddedededah EdedededaH edededehdahdahdah)
We create our own
Your own reality
Everything in the world
Is reflection of the me
Use your energy for something new un-thought
Do what you always did
You'll get what you always got
(Eddedededah EdedededaH edededehdahdahdah)
Go with me down
All the way down to the bottom
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Go with me down
All the way down to the bottom
Where you will, find your crown
Your love your fear and all that is rotten
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[Chorus 2x]
(Eddedededah EdedededaH edededehdahdahdah)
We create our own
Your own reality
Everything in the world
Is reflection of the me
Use your energy for something new un-thought
Do what you always did
You'll get what you always got
(Eddedededah EdedededaH edededehdahdahdah)
Go with me down
All the way down to the bottom
Where you will, find your crown
Your love your fear and all that is rotten
Go with me down
All the way down to the bottom
Where you will, find your crown
Your love your fear and all that is rotten