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.