00:01
For this problem, we want to approximate the area under the graph of f, which is equal to the square root of x squared minus 1, over the closed interval 2 to 4, using simpson's rule and four subintervals.
00:13
Now, let's recall the simpson's rule.
00:16
In simpson's rule, the integral from a to b of f of x, dx, that's the area of the region under the curve f over the interval a to b is approximately 1 third of d.
00:30
Delta x or that's one -third of b minus a over n times f of x of 0 plus 4 times f of x of 1 plus 2 f of x of 2 and so on and then plus 4 times f of n minus 1 plus f of x of n.
00:46
In this formula we have to find our delta x so that we can find our points x of 0 x sub 1 and so on.
00:55
Now if our interval is 2 to 4 and our n is equal to 4 then our delta x will be equal to b minus a over n, that's 4 minus 2 over 4, which is equal to 1 half.
01:10
So our x -0, the initial point, is equal to 2.
01:15
X sub 1 will be 1 1 half from 2, that's 2 plus 1 half or 2 .5...