00:01
Hi, to answer this question for the first part, we are given with l10 for fx that is equals to under root of 4 minus x square on an interval from minus 2 to 2.
00:14
Here we can see we need to write it in sigma notation as a sum and here this is a left remand sum where n is equals to 10 and a is equals to minus 2 and b is equals to 2.
00:27
So first we can find the value for delta x that will be equals to b minus a by n and it is equals to 2 minus minus 2 by 10 and this is equals to 4 by 10 or we can write it as 2 by 5.
00:41
Now as we are given with the function f xi that can be represented as under root of 4 minus xi square or we can write first for x1 our function here will be under root of 4 minus xi square.
00:57
4 minus x1 square where x1 can be calculated as minus 2 plus 2 by 5 times here we multiply it by 0 now solving this further we get x1 to be equals to minus 2 next x2 will be equals to minus 2 plus 2 by 5 times 1 and this will be equals to for x 3 we can write minus 2 plus 2 by 5 times 1 and this will be equals to for x 3 we can write minus 2.
01:30
Minus 2 plus 2 by 5 times 2 and similarly for x i we can write minus 2 plus 2 by 5 times i minus 1 since for 3 it is 2 over here so we can replace the function f of x i to be equals to under root of 4 minus minus 2 plus 2 by 5 times i minus 1 whole square so from here we can write the left remand sum as our final answer that l 10 will be equals to delta x which is 2 by 5 times summation from i is equals to 1 to 10.
02:08
Here we have under root of 4 minus minus 2 plus 2 by 5 times i minus 1 and whole square.
02:20
Next to solve for the next part we need to express the given results in terms of limits as integral.
02:31
We are given with limit, n approaches to infinity, summation i is equals to 1 to n, cos square 2 pi x i delta x over an interval from 0 to 1...