00:01
Hello everyone, in this problem we are going to evaluate the integral which is given as integral over 0 to b 5 into e power x dx where we are given with the value of b as 5 .75.
00:17
So now according to simpson's rule, so which states that integral over a to b f of x dx can be approximately equal to del x by 3 of f of x naught plus 4 f x1 plus 2 f x2 plus 4 f x3 plus 2 f x4 plus and so on plus 2 of f xn minus 2 plus 4 f of xn minus 1 plus f of xn where del x is given by the formula b minus a divided by n.
01:17
So here we have the value of a to be 0, b as 5 .75 which can be written as 23 by 4 and here n is given as 4.
01:31
So now substituting the values in del x we have the value of del x to be 23 by 4 minus 0 divided by 4.
01:41
So simplifying this we have the value as 23 by 16.
01:45
Now we divide the interval 0 to 23 by 16 into 4 sub intervals of length 23 by 16 with the end points a to be 0, 23 by 16, 23 by 8, 69 by 16 and 23 by 4 which is to be b.
02:21
Now we just evaluate the function at these end points.
02:31
So f of x naught which is nothing but f of a and its value will be f of 0 and here f of x value is f of x is given that 5 into e power x.
02:49
Now substituting the value of x as 0 in the given f of x so we have 5 into e power 0.
02:56
So simplifying this we have the value as 5.
03:00
Similarly 4 of f x1 here x1 is 23 by 16 so there is 4 of f of 23 by 16.
03:10
Substituting the value of x as 23 by 16 in the given f of x so we will be getting as 5 into e power 23 by 16.
03:19
So simplifying this it will be equal to 84 .2031451228792...