Text description - screencast for interactive 2

[In this video, an electronic x and y graph is used to show how equations can be presented in graph form. Below the graph, adjustable sliders allow individual values in the equation to be changed. On the graph, a line curves upwards from the x-axis. A series of shaded rectangles run along the x-axis, their top right corners intersecting with the line. As the values in the equation are changed, the shape of the graph changes and also figures marked "Area of rectangles", "Total area of rectangles and "Actual area under graph" change. The narrator describes the changes.]

NARRATOR: In this interactive, we explore the right endpoint estimate. Here, we're looking at the graph of y = x squared + 1 and we're looking at estimating the area under that graph from x = 0 up to x = 5. Currently, n is set to 5, which means we've divided this region into five rectangles of equal width. We note that over this interval, the graph of y = x squared + 1 is an increasing function and so this means that the right endpoint estimate is in fact an overestimate of the actual area under this graph.

We see as we increase the value of n, we're increasing the number of rectangles and we're hence making each of those rectangles thinner, which we see being calculated here with delta x, and we also see that the area given by these rectangles is getting closer and closer and closer to the actual area and we can see that both graphically up above and numerically down in the bottom left-hand corner here. And we see that the more rectangles we create, the closer and closer and closer this right endpoint estimate is as an approximation of the actual area.