00:01
Here i'll discuss how you would set up and work out a rhyme -on sum.
00:07
And the rhyme -on -sum of a function is approximating the area under the curve f of x between two limits.
00:29
We'll call them a and b using small rectangles.
00:40
And i'll show what those rectangles look like in a little bit.
00:43
And how you set up that.
00:48
So here's our function, f of x, and ordinarily you'd have a formula for that or an equation.
00:56
And we're evaluating the area between point a and b, and i do note that f of x must be a function.
01:03
It must be single -valued for each value of x.
01:06
There is a unique value.
01:11
So that's what we mean by a function.
01:13
But you first start off and you figure out how many rectangles you're going to use.
01:19
And for the sake of argument, let's suppose n equals four rectangles.
01:29
So the first step is to divide a, the region between b and a into four pieces.
01:44
So here we're going to divide it hopefully into four relatively equal rectangles.
01:52
Okay.
01:53
So the base of each rectangle has the value.
01:57
We'll call that delta x is equal to b minus a divided by n.
02:04
In this case, n is four.
02:06
And those should be a little bit more equal looking.
02:09
So each of those has a width delta x.
02:14
Now for the height of the rectangle, you have a choice.
02:20
You can either use the left value f of x left or right value f of x right, or you can use them both and do sort of an average.
02:47
But let's take a look at the left value left endpoints...