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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.
Metadata describing this Open University video programme
Module code and title: M101, Mathematics: a foundation course
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