00:01
Hi, in the given question we have to use trapeze idol for integral over 0 to 2 x cubed into d x for n is equal to 4.
00:14
We know that the trapeze hurdle t n is approximately equals to integral over a to b f of x into d x.
00:26
Comparing this two equations we get a is equal to 0 and b is equal to 2.
00:34
Then the trapeze hurdle is given by tn is equal to delta x upon 2 in bracket f of x0 plus 2 f of x1 plus 2 f of x2 plus up to f of x n.
00:55
Now simplifying this, we get delta x is equal to b minus a upon 2.
01:03
That is we have 2 minus 0 upon 2 which is equal to 2 by 2 that is 1.
01:10
So, simplifying the given trapeze hurdle for the given rule, we get delta x is equals to 1.
01:19
Now in the question we have given for n is equal to 4.
01:23
We have 2 divide this interval 0 to 2 for n is equal to 4.
01:29
Therefore we get x0 is equal to 1 by 2 comma x1 is equal to 1 x2 x2 is equal to 3 by 2 and x4 is equal to 2.
01:44
Therefore for the given integral we have the trapezole is equal t of 4 is approximately equal to our delta x4.
01:55
X is 1 by 2 in bracket f of 1 by 2 plus 2 times f of 1 plus 2 times f of 2 5 of 3 by 2 plus f of 2 since our x 4 that is for n is equal to 4 our last term is 2 which is a required trapezzarder next we have to find the approximate value of integral over 2 2 2 f of x d x by using the given table...