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Resource type Integration as a summation
The 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.
Resource type Integration as a summation
The 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) This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Resource type Finding areas by integration
This unit looks at how to calculate the area bounded by a curve using integration.
Resource type Integration as a summation
The 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.
Resource type Integration by substitution
There 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.
Resource type Integration by parts
A 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.
Resource type Integration by substitution
There 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.
Resource type Integration as summation
An 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)
Resource type Integration as the reverse of differentiation
This 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.
Resource type Integration by parts
A 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.
Resource type Integration as the reverse of differentiation
This 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.
Resource type Integration by parts
A 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.
Resource type Diagnostic test in basic calculus - Numbas
12 calculus questions, differentiation and integration. Useful for self diagnosis. Numbas resources have been made available under a Creative Commons licence by Bill Foster and Christian Perfect, School of Mathematics & Statistics at Newcastle University.
Resource type 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).
Resource type Integration that leads to logarithms
The 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.
Resource type 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).
Resource type Integration by parts
This 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)
Resource type Finding areas by integration
Integration can be used to calculate areas. In simple cases, the area is given by a single definite integral. But sometimes the integral gives a negative answer which is minus the area, and in more complicated cases the correct answer can be obtained only by splitting the area into several parts and adding or subtracting the appropriate 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.
Resource type Integration: Laplace Transforms
Reviews the techniques of integration needed to find and manipulate Laplace Transforms. This Quick Reference leaflet is contributed to the mathcentre Community Project by Leslie Fletcher and reviewed by Martin Randles, Liverpool John Moores University.
Resource type Finding areas by integration
Integration can be used to calculate areas. In simple cases, the area is given by a single definite integral. But sometimes the integral gives a negative answer which is minus the area, and in more complicated cases the correct answer can be obtained only by splitting the area into several parts and adding or subtracting the appropriate 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.
Resource type Diagnostic Test: Indefinite Integration - Numbas
16 questions: Inverse of differentiation, substitution, inverse trig functions, partial fractions and by parts. For those that want a thorough testing of their basic techniques in integration. Numbas resources have been made available under a Creative Commons licence by the School of Mathematics & Statistics at Newcastle University.
Resource type Indefinite integration by substitution - Numbas
5 questions on using substitution to find 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.
Resource type Integration by substitution
This unit explain integration by substitution.
Resource type Integration by substitution
Some 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)
Resource type Integration as the reverse of differentiation
This unit explain integration as the reverse of differentiation.
Resource type Integration that leads to log functions
This 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.

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