00:01
In this question, we have to find the smallest value of n, correct, such that mn is always less or equals to 0 .005 for the definite integral 0 to 1 x square minus 1 times of dx.
00:20
So basically here we are using the midpoint rule.
00:23
Okay, we say which says that mod of em less or equals to k times b minus a whole cube over 24 n square.
00:36
Okay, and it is also given that f double dash of x is less or equals to k.
00:44
So from this we take f of x as x square minus 1.
00:51
So since we have f of x as x square minus 1, this implies f dash of x will be just 2x and f double dash of x equals to 2, which further implies that triple dash of x equals to 0.
01:09
Now what we can do is we try to find since you see k value is always greater or equals to f double dash.
01:19
So f double dash at x equals to zero it comes out to be two only and one at the extreme points we are finding it is also equals to two correct.
01:31
So from these two we know the k is maximum of these two correct.
01:37
So k is the maximum of f double dash 0 mod of f double dash 0 and mod of f double dash 1 so both are equals to 2 so we get the value of k as hence we get mod of e m is less or equals to e m is the error which is less or equals to k is to to b minus a...