Integration resources

A Calculus Refresher. This booklet revises techniques in calculus (differentiation and integration). This is a welsh language version

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)

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)

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.

This resource covering the Trapezium Rule, Simpsons Rule and an overview of error function has been contributed to the mathcentre Community Project by Josh Simpson and reviewed by Leslie Fletcher, Liverpool John Moores University.

This unit looks at how to calculate the area bounded by a curve using integration.

This unit explain integration as the reverse of differentiation.

This unit explain integration by substitution.

We 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.

In 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.

We 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.

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.

4 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 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.

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.

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.

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.

We 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.

We 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.