**Description**

This programme introduces the idea of an area-so-far function, and uses the relationship between this function and its original function to show that primitives can be used as a means for working o...ut intergals.

Module code and title: | M101, Mathematics: a foundation course |
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Item code: | M101; 13 |

First transmission date: | 21-05-1978 |

Published: | 1978 |

Rights Statement: | |

Restrictions on use: | |

Duration: | 00:23:58 |

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Producers: | John Jaworski; Jean Nunn |

Contributors: | Graham Read; Allan I.,1936-2013 Solomon |

Publisher: | BBC Open University |

Keyword(s): | Area calculation; Calculus; Cosine function; Fundamental Theorem; Primitives |

Footage description: | Graham Read introduces the programme. Allan Soloman works through some problems from the unit text, he plots a function and then the derived function and then an area-so-far function which compares to the original function. Graham Read points out that working out areas under curves using a limit of a sum of rectangles method, can become difficult. Alan Solomon, with the aid of computer animations demonstrates how an area-so-far function can be arrived at, and that it can give values for the area between any two points. Graham Read, using computer animations, shows that as I tends to O the derivative of A at X has the same value as f(x). He uses this result to find an area under the curve f(X) = COS X. He checks to establish that the sine function is an area-so-far function, and then shows that by finding primitives we have a simple method for working out integrals, a rule known as the fundamental theorem of calculus. |

Master spool number: | 6HT/72528 |

Production number: | 00525_4250 |

Videofinder number: | 2468 |

Available to public: | no |