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Integration as a summationThe second major component of the Calculus is called integration. This
may be introduced as a means of finding areas using summation and limits. We
shall adopt this approach in the present Unit. In later units, we shall also
see how integration may be related to differentiation. (Mathtutor Video Tutorial)
The video is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Integration as summationAn integral is defined as an infinite sum. This leaflet explains how this is done. This notion is important when we want to apply integration in many fields. (Engineering Maths First Aid Kit 8.12)
Integration as the reverse of differentiationIntegration is introduced here as the reverse of differentiation. (Engineering Maths First Aid Kit 8.6)
Integration as the reverse of differentiationThis unit explain integration as the reverse of differentiation.
Integration as the reverse of differentiationThis unit explain integration as the reverse of differentiation. (Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Integration as the reverse of differentiationThis unit explain integration as the reverse of differentiation. (Mathtutor Video Tutorial)
The video is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Integration by partsThis leaflet explains integration by parts. This is a technique for integrating a product of two functions (two functions multiplied together). (Engineering Maths First Aid Kit 8.10)
Integration by partsA special rule, integration by parts, is available for integrating
products of two functions. This unit derives and illustrates this rule with a
number of examples.
Integration by partsA special rule, integration by parts, is available for integrating
products of two functions. This unit derives and illustrates this rule with a
number of examples. (Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Integration by partsA special rule, integration by parts, is available for integrating
products of two functions. This unit derives and illustrates this rule with a
number of examples. (Mathtutor Video Tutorial)
The video is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Integration by Parts - Numbas4 questions on integrating by parts. Numbas resources have been made available under a Creative Commons licence by Bill Foster and Christian Perfect, School of Mathematics & Statistics at Newcastle University.
Integration by substitutionSome integrals can be evaluated by making an appropriate substitution to change the variable. This leaflet explains how this can be done. (Engineering Maths First Aid Kit 8.11)
Integration by substitutionThere are occasions when it is possible to perform an apparently difficult piece of integration by first making a
substitution. This has the effect of changing the variable and the integrand. When dealing with definite integrals,
the limits of integration can also change.
In this unit we will meet several examples of integrals where it is appropriate to make a substitution. (Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Integration by substitutionThere are occasions when it is possible to perform an apparently difficult piece of integration by first making a
substitution. This has the effect of changing the variable and the integrand. When dealing with definite integrals,
the limits of integration can also change.
In this unit we will meet several examples of integrals where it is appropriate to make a substitution. (Mathtutor Video Tutorial)
The video is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Integration for Economics and Business Studies Overview of the rules of integration and their applications in Economics and Business Studies. This leaflet has been contributed to the mathcentre Community Project by Morgiane Richard (University of Aberdeen) and reviewed by Anthony Cronin (University College Dublin).
Integration for Economics and Business Studies (SOURCE)Latex source, image files and metadata for the Fact & Formulae leaflet "Integration for Economics and Business Studies " contributed to the mathcentre Community Project by Morgiane Richard (University of Aberdeen) and reviewed by Anthony Cronin (University College Dublin).
Integration that leads to log functionsThis unit is concerned with integrals which lead to logarithms.
Whenever the integrand is fraction with denominator f(x) and numerator f'(x)
the result of integrating is the natural logarithm of f(x). This unit illustrates this
behaviour with several examples. (Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Integration that leads to log functionsThis unit is concerned with integrals which lead to logarithms.
Whenever the integrand is fraction with denominator f(x) and numerator f'(x)
the result of integrating is the natural logarithm of f(x). This unit illustrates this
behaviour with several examples. (Mathtutor Video Tutorial)
The video is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Integration that leads to logarithmsThe derivative of ln x is 1/x. As a consequence, if we reverse
the process, the integral of 1/x is ln x+c. In this unit we
generalise this result and see how a wide variety of integrals result in
logarithm functions.
Integration using a table of anti-derivativesWe may regard integration as the reverse of differentiation. So if we have
a table of derivatives, we can read it backwards as a table of
anti-derivatives. When we do this, we often need to deal with constants
which arise in the process of differentiation.
Integration using a table of anti-derivativesWe may regard integration as the reverse of differentiation. So if we have a table of derivatives, we can read it backwards as a table of anti-derivatives. When we do this, we often need to deal with constants
which arise in the process of Differentiation. (Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Integration using a table of anti-derivativesWe may regard integration as the reverse of differentiation. So if we have a table of derivatives, we can read it backwards as a table of anti-derivatives. When we do this, we often need to deal with constants
which arise in the process of Differentiation. (Mathtutor Video Tutorial)
The video is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Integration using partial fractions 1Sometimes the integral of an algebraic fraction can be found by first expressing the algebraic fraction as the sum of its partial fractions. In this unit we will illustrate this idea. We will see that it is also necessary to draw upon a wide variety of other techniques such as completing the square, integration by substitution, using standard forms, and so on.
Integration using partial fractions 2In this unit we are going to look at how we can integrate some more algebraic fractions. We shall concentrate on the case where the denominator of the fraction involves an irreducible quadratic factor. The case where all the factors of the denominator are linear has been covered in the first unit on integration using partial fractions.
Integration using trig identities and trig substitutions.This unit explains how trig identities and trig substitutions can help when finding integrals.
