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graphThe integral of y with respect to x is \displaystyle \int y \, dx .
When definite integration is used to find areas, notation like \displaystyle \int_a^b y \, dx is used where the a and b denote the lower and upper limits of the integration.

You must understand clearly how integral notation works. When doing definite integration, use the notation as accurately as you can, including the use of different styles of brackets.
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Summary/Background

graphic calculatorA note about graphic calculators
A graphic calculator, for example the TI-83 or similar model, can work out definite integrals for you.

definite integrationFirst use the Y= screen to enter a function, such as -X²+9x-14
Use ZOOM 6 to get a good display of the curve.
Select 2nd CALC option 7.
Enter the lower and upper limits of the integration as requested on the screen.

Software/Applets used on this page

jsMath
This page uses jsMath
You can get a better display of the maths by downloading special TeX fonts from jsMath. In the meantime, we will do the best we can with the fonts you have, but it may not be pretty and some equations may not be rendered correctly.

Glossary

function

A rule that connects one value in one set with one and only one value in another set.

integral

the anti-derivative

integration

the process of finding an integral, the reverse process to differentiation.

union

The union of two sets A and B is the set containing all the elements of A and B.

work

Equal to F x s, where F is the force in Newtons and s is the distance travelled and is measured in Joules.

Full Glossary List

This question appears in the following syllabi:

SyllabusModuleSectionTopic
AP Calculus AB (USA)4IntegrationDefinite integration
AP Calculus BC (USA)4IntegrationDefinite integration
AQA A-Level (UK - Pre-2017)C1IntegrationDefinite integration
AQA AS Maths 2017Pure MathsIntegrationDefinite Integration and Areas
AQA AS/A2 Maths 2017Pure MathsIntegrationDefinite Integration and Areas
CBSE XII (India)CalculusIntegralsEvaluation of definite integrals
CCEA A-Level (NI)C2IntegrationDefinite integration
CIE A-Level (UK)P1IntegrationDefinite integration
H IntegrationH3 Definite Integrals and AreasDefinite Integration and Areas
Edexcel A-Level (UK - Pre-2017)C2IntegrationDefinite integration
Edexcel AS Maths 2017Pure MathsIntegrationDefinite Integration and Areas
Edexcel AS/A2 Maths 2017Pure MathsIntegrationDefinite Integration and Areas
I.B. Higher Level6IntegrationDefinite integration
I.B. Standard Level6IntegrationDefinite integration
Methods (UK)M9IntegrationDefinite integration
OCR A-Level (UK - Pre-2017)C2IntegrationDefinite integration
OCR AS Maths 2017Pure MathsIntegrationDefinite Integration and Areas
OCR MEI AS Maths 2017Pure MathsIntegrationDefinite Integration and Areas
OCR-MEI A-Level (UK - Pre-2017)C2IntegrationDefinite integration
Pre-U A-Level (UK)5IntegrationDefinite integration
Scottish (Highers + Advanced)HM2IntegrationDefinite integration
Scottish HighersM2IntegrationDefinite integration
Universal (all site questions)IIntegrationDefinite integration
WJEC A-Level (Wales)C2IntegrationDefinite integration