00:01
In this problem, we want to determine a region whose area is equal to the given limit.
00:05
So here we have the limit for n approx to infinity of the sum of 1 over n times i over n to the power of 4, for i ranging between 1 to n.
00:16
So what you recall here is that an integral corresponds or gives us the area of a region, and that the definition of an integral is in fact the limit of a sum.
00:29
So let's write the definition of an integral.
00:31
The integral of f of x dx for x ranging between a to b is defined as the limit when n approaches to infinity of the sum of f of xi times delta x for i ranging from 1 to n, where delta x corresponds to the spacing of our intervals defined as b minus a divided by n, where n corresponds to the number of intervals that we are partitioning our region, and xi corresponds to the partitioning value of x, which is defined, generally speaking, using the endpoint rule as a plus b minus a divided by i, divided by n, times i divided by n.
01:42
And we know that this form of limit is very similar to what we have.
01:48
So in our problem, we have the limit when n approaches to infinity of the sum of 1 over n times i over n to the power of 4, for i ranging from 1 to n.
02:05
So the terms with i correspond to f of xi...