00:01
In this problem, we're supposed to use the following table to estimate the integral from 0 to 20.
00:09
So the question we first have to ask ourselves is, how will we be able to use this to estimate the integral? so we have some sort of function that looks something like this, right, over the interval from 0 to 20.
00:31
And we first noticed that it's partitioned by fours.
00:36
We have 4, 8, 12, 16, and then 20.
00:46
So the question is, how do we estimate integrals? we estimate them by doing the area.
00:54
So we can use left hand estimates, or we can use right hand estimates.
00:59
So i say let's use a right hand estimate here.
01:03
We could also use midpoint estimates, but we cannot do that in this case because we don't know what the midpoint of each of these is, since we only have the end points at 0, 4, 8, 12, 16, and 20.
01:22
So we can estimate the area, the integral, by finding the area of these rectangles.
01:30
This again is a right -hand sum.
01:38
We could do a left -hand sum in which we will use the left -hand points.
01:47
So at the left -hand, we go up to the function, that determines our height.
01:50
The left -end point go up to the function, that determines our height.
01:56
At the left end point, we go up to the function, determines our height.
02:01
At the left end point determines our height, left endpoint determines our height.
02:11
So either one will be able to get us a estimation.
02:18
So why don't we just do the right hand some? so we say for that first rectangle, zero to four, what is the height? what is the height of my function at the right endpoint? well, that is 56.
02:36
What is the width of my rectangle for? what about my second rectangle? so i use the right endpoint, go up to the function...