# Integration by substitution resources

### Practice & Revision (2)

Cwrs Gloywi Calcwlws

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

### Quick Reference (1)

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)

### Staff Resources (1)

Maths EG Teacher Interface

The teacher interface for Maths EG which may be used for computer-aided assessment of maths, stats and numeracy from GCSE to undergraduate level 2. These resources have been made available under a Creative Common licence by Martin Greenhow and Abdulrahman Kamavi, Brunel University. Teachers need to register (top right of screen) and thereafter login to use the system, after which they may use it to compose their own tests by selecting (specifically or randomly) questions from the entire database of questions. Instructions are available from the title page.

### Teach Yourself (1)

### Test Yourself (5)

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.

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.

Diagnostic Text - Integration by substitution

This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

Exercise - Integration by substitution

This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.

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.

### Video (1)

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.