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In this interactive,

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we explore the right
endpoint estimate.

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Here, we're looking at the graph

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of y = x squared + 1

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and we're looking at estimating

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the area under that graph

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from x = 0 up to x = 5.

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Currently, n is set to 5,

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which means we've divided this region

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into five rectangles of equal width.

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We note that over this interval,

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the graph of y = x squared + 1

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is an increasing function

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and so this means

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that the right endpoint estimate

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is in fact an overestimate

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of the actual area under this graph.

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We see as we increase the value of n,

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we're increasing

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the number of rectangles

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and we're hence making

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each of those rectangles thinner,

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which we see being calculated

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here with delta x,

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and we also see that the area

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given by these rectangles is getting

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closer and closer and closer

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to the actual area

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and we can see that

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both graphically up above

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and numerically down in the bottom

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left-hand corner here.

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And we see that the more

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rectangles we create,

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the closer and closer and closer

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this right endpoint estimate is

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as an approximation
of the actual area.