00:01
In this question, we need to use the simpson rule to find out the value of the approximation and the errors.
00:08
Okay, so here we have to use this simpson rule for the following value of n, which is given as 4, 8, 16 and 32.
00:19
And we have been given the exact value of this integral, which is 0 to 4, 9x, raise to 5, minus 4x cube, dx.
00:29
It is given to be 5 triple 8.
00:33
Okay, so let us see how we are going to do this.
00:37
So first of all, how we are going to apply the simpson rule.
00:40
Let us write down the formula for it.
00:43
So we know that here f of x will be what.
00:46
So here we will take f of x to be 9x raised to 5 minus 4x cube.
00:52
Correct.
00:53
And then from simpson rule, what is the value of s4? so s4 is given by delta of x divided by three times f of 0 plus 4 times f of 1 plus 2 times f of 2 plus 4 times f of 3 and plus f of 4.
01:20
So this is the value of s4.
01:23
This i'm computing for n equals to 4.
01:26
And here what is the value of delta of x? so delta of x is nothing but b minus a divided by n.
01:33
B is so this is the value of a and this is the value of b so b is 4 a is 0 divided by n which is 1 here so delta x comes out to be 1 correct now what i will do i will take my x not to be 0 x1 to be 1 okay similarly x2 i will take as 2 x3 will be 3 and similarly x 4 i will assume it as 4 and then i i'll try to find out the value of the function at these x -is.
02:08
Okay, so let us see how we are going to do this.
02:13
So using this, what i am going to get is the following things.
02:19
Let me write down this table...