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.

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

## 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.

## This question appears in the following syllabi:

Syllabus | Module | Section | Topic |
---|---|---|---|

AP Calculus AB (USA) | 4 | Integration | Definite integration |

AP Calculus BC (USA) | 4 | Integration | Definite integration |

AQA A-Level (UK - Pre-2017) | C1 | Integration | Definite integration |

AQA AS Maths 2017 | Pure Maths | Integration | Definite Integration and Areas |

AQA AS/A2 Maths 2017 | Pure Maths | Integration | Definite Integration and Areas |

CBSE XII (India) | Calculus | Integrals | Evaluation of definite integrals |

CCEA A-Level (NI) | C2 | Integration | Definite integration |

CIE A-Level (UK) | P1 | Integration | Definite integration |

H Integration | H3 Definite Integrals and Areas | Definite Integration and Areas | |

Edexcel A-Level (UK - Pre-2017) | C2 | Integration | Definite integration |

Edexcel AS Maths 2017 | Pure Maths | Integration | Definite Integration and Areas |

Edexcel AS/A2 Maths 2017 | Pure Maths | Integration | Definite Integration and Areas |

I.B. Higher Level | 6 | Integration | Definite integration |

I.B. Standard Level | 6 | Integration | Definite integration |

Methods (UK) | M9 | Integration | Definite integration |

OCR A-Level (UK - Pre-2017) | C2 | Integration | Definite integration |

OCR AS Maths 2017 | Pure Maths | Integration | Definite Integration and Areas |

OCR MEI AS Maths 2017 | Pure Maths | Integration | Definite Integration and Areas |

OCR-MEI A-Level (UK - Pre-2017) | C2 | Integration | Definite integration |

Pre-U A-Level (UK) | 5 | Integration | Definite integration |

Scottish (Highers + Advanced) | HM2 | Integration | Definite integration |

Scottish Highers | M2 | Integration | Definite integration |

Universal (all site questions) | I | Integration | Definite integration |

WJEC A-Level (Wales) | C2 | Integration | Definite integration |