The animation shows how an integral can be approximated by establishing upper and lower sums. The shape of the curve can be modified by moving the gray circles on either side.

To display the root function, click on the large rectangle with the content. The values in the table at the top right can be changed.

The number of subdivisions can also be changed. The higher the number of subdivisions, the finer the gradations of the upper and lower totals. In the case of a very high number of subdivisions, no difference to the shape of the curve is discernible. The total areas then almost correspond to the integral.

The second table shows the calculated values for the total area of the upper sums, the lower sums and finally the integral itself. By increasing the number of subdivisions, it can be observed that the value of the total area of all subtotals and also of the subtotals approximates the value of the integral. The upper sums approach the value of the integral from above, the lower sums approach the value of the integral from below.

## Overview and Download

Title | Fundamentals of integral calculus |

Target audience | Teachers and lecturers |

Plattformen | Microsoft® Windows® Apple® Macintosh® |

Features | Full screen mode Lossless magnification Large screens supported |

License | Freeware (for non-commercial use) |

Download | Microsoft® Windows® Apple® Macintosh® |

## Sources

Authoring tool: Adobe Animate