# 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)

### Teach Yourself (1)

### Test Yourself (3)

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.

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.