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The 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.

## Summary/Background

 A note about graphic calculatorsA graphic calculator, for example the TI-83 or similar model, can work out definite integrals for you. First use the Y= screen to enter a function, such as -X²+9x-14Use 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

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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:

SyllabusModuleSectionTopicExam Year
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-
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-