Available online
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.
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 |
|---|---|
| Item code: | M101; 13 |
| First transmission date: | 21-05-1978 |
| Published: | 1978 |
| Rights Statement: | |
| Restrictions on use: | |
| Duration: | 00:23:58 |
| + Show more... | |
| 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 |
