00:01
Okay, in this question, we are required to approximate this integral, i mean the integral goes from one to six of fx by its riemann sum.
00:13
Okay, let's first recall what a riemann sum is.
00:18
Suppose we have a function, let's call it gx, and the graph of gx will be like this, and the riemann sum will be some sum of some rectangle, right, sum of many rectangles.
00:35
What do i mean, suppose? i mean that, let's assume this is one, and this is six.
00:50
The riemann sum from one to six will be some rectangle like that, will be some rectangle like that.
01:16
And here, the length of this interval will be delta j, delta j, we don't require all the delta j's to be equal, but in most of the questions, for our convenience, we just use some equal length delta.
01:42
This is a riemann sum with the left endpoint, because we always use the left point.
01:56
Okay, and what about the right point, if we want to use the right endpoint, then our graph will be like that.
02:10
So here, as we are given some values of fx, and you can see all the lengths are equal, i mean, we want to use a very special riemann sum with all the deltas are equal.
02:26
That means to approximate this one, we only need to consider some value of function from one to six, but, i mean, however, as we only want to consider the left endpoint, we actually only need the value of fx from one, two, three, four...