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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 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 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 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 using partial fractions - Numbas4 questions on using partial fractions to solve indefinite integrals. 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 using trig identities or a trig substitutionThis unit explains how trig identities and trig substitutions can help when finding integrals. (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: Laplace Transforms SOURCEA zip file containing LaTeX source and eps files for the quick reference leaflet 'Integration: Laplace Transforms' contributed to the mathcentre Community Project by Leslie Fletcher, Liverpool John Moores University
Integration using trig identities or a trig substitutionThis unit explains how trig identities and trig substitutions can help when finding integrals. (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 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.
Linearity rules of integrationThis leaflet explains how to integrate the sum of two functions, and constant multiples of functions, using 'linearity rules'. (Engineering Maths First Aid Kit 8.8)
Cwrs Gloywi CalcwlwsA Calculus Refresher.
This booklet revises techniques in calculus (differentiation and integration).
This is a welsh language version
Integration as the reverse of differentiationIntegration is introduced here as the reverse of differentiation. (Engineering Maths First Aid Kit 8.6)
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 trig identities and trig substitutions.This unit explains how trig identities and trig substitutions can help when finding integrals.
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 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.
Integrating algebraic fractions (1)Sometimes 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. (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.
Integrating algebraic fractions (1)Sometimes 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. (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.
Integrating algebraic fractions (2)Sometimes 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 look at the case where the denominator of the fraction involves an
irreducible quadratic expression. (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.
Integrating algebraic fractions (2)Sometimes 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 look at the case where the denominator of the fraction involves an
irreducible quadratic expression. (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.
First order differential equations - Numbas9 questions on first order differential equations. Straight forward integration (2), separating variables (4), linear (1), homogenous (2). All are either initial value or boundary value problems. Numbas resources have been made available under a Creative Commons licence by Bill Foster and Christian Perfect, School of Mathematics & Statistics at Newcastle University.
Volumes of solids of revolutionWe sometimes need to calculate the volume of a solid which can be obtained by
rotating a curve about the x-axis. There is a straightforward technique
which enables this to be done, using integration. This unit will explain how.
Volumes of solids of revolutionWe sometimes need to calculate the volume of a solid which can be obtained by
rotating a curve about the x-axis. There is a straightforward technique
which enables this to be done, using integration. (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.
Volumes of solids of revolutionWe sometimes need to calculate the volume of a solid which can be obtained by
rotating a curve about the x-axis. There is a straightforward technique
which enables this to be done, using integration. (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.
