00:01
This problem is asking us to find the area under the curve from 4 to 12 of the function f of x equals 0 .04x to the 4th minus 3 .24x squared plus 92.
00:13
I'm drawn a sketch of the graph over here to the right.
00:16
We're interested in estimating this area under the curve from 4 to 12, so the area on the right of the graph over there.
00:26
We're asked to do this using four sub -interval.
00:30
That i need to do is determine how wide i want each of my groups to be.
00:34
We're going to evaluate that using that b minus a over n.
00:40
That's my delta x or my change in x.
00:43
For this problem, the b value is 12, the a value is 4, and i want four sub -intervals.
00:50
12 minus 4 divided by 4 is 2.
00:52
So the width of each one of the rectangles that i'm going to create is two units wide, which means i'm going to be going from four to six, six to eight, eight to ten, and ten to twelve.
01:04
So if i draw in my lines showing my heights for each one of those, and then we can, we're wanting to use a left -hand ream on some, which means each one of my rectangles height needs to depend on the left -hand side.
01:19
So our rectangles are going to be these rectangles here.
01:28
And of course, this picture is not drawn to scale.
01:30
I just sketched it.
01:31
So the idea here is to find the area of each one of these rectangles, and that will give me an approximation for the area under the curve.
01:40
Now, i know the width of each rectangle is two, but i need to know the height of each rectangle.
01:45
The first rectangle has a height that is based at f of 4.
01:52
The second rectangle is a height based at f of 6.
01:57
The third rectangle has a height at f of 8, and the fourth rectangle has a height evaluated at f of 10, function value at 10...