00:01
In this question, we are given that the value of integral from 0 to 1, f of x, dx is equal to 0 .5.
00:11
We need to calculate the value of f of 0 .5.
00:17
If we are given that h is equal to 0 .25, f of 1 is equal to f of 0 .25 is equal to 1, and f of 0 .25 is equal to 1.
00:32
75 is equal to 0 .25 by using the tiptozoidal rule.
00:41
Now the formula for tiptoid rule is given by from a to b, f of x bx is equal to 1 over 2 times h times y0 plus 2 times of y1 plus y2 plus y3 plus 1 plus 1 plus 1 up to yn minus 1.
01:07
Plus y n where h is equal to b minus a over n now according to the given question h is 0 .25 b is equal to 1 and a is equal to 0 therefore the value of n would be 1 minus 0 over 0 .25 that is 4 therefore the value of n is 4.
01:39
Now, substituting the values in reprozoidal rule, we get 0 to 1, f of x d x is equal to hz, that is 0 .25 over 2 times y not, that is f of 0 plus 2 times 0 .25 plus f of 0 .25 plus f of 0 .75, plus f of 0 .75, plus f of 0 .75, plus f of 0 .5, plus f of 0 .5, plus f of 0 .5, plus f of 0.
02:16
F of 1.
02:19
For the solving we get 1 over 8 times f of 0 is 0 plus 2 times f of 0 .25 is given as 1 plus f of 0 .25 plus 0 .75 plus f of 0 .75 is 0 .25 plus 1.
02:38
Also the value of integral is 0 .5.
02:43
Cross multiplying we get 4 is equal to 2 times 2.
02:47
Of 1 .25 plus f of 0 .5 plus f of 0 .5 plus 1.
02:59
Purpose solving we get 3 to 2 .5 plus 2 times 4 f of 0 .5.
03:11
That is 0 .5 would be equal to 2 times f of 0 .5 .5...