00:01
We want to use simpson's rule to estimate the integral from 9 to 27 of f of x dx given the table.
00:07
We have simpson's rule up here shown, um, where the integral from a to b of f of x dx is delta x over 3 times f of x of 0 plus 4 times f of x of 1 plus 2 times f of x of 2.
00:21
In the coefficients of the function just alternate between 4 and 2.
00:25
The second to the last term would have a function of, uh, coefficient of 4 times f of x of n minus 1 and then plus regular f of x of n or the function at the nth term.
00:36
So n, we need to figure out what our n value is, which means the number of rectangles that would be if we graph these points on the coordinate plane, um, this data on the coordinate plane.
00:50
And we would have the interval from 9 to 27 and if we show the subintervals we'd have one interval from 9 to 12, an interval from, subinterval from 12 to 15, one from 15 to 18, from 18 to 21, from 21 to 24, and from 24 to 27.
01:05
That is 1, 2, 3, 4, 5, 6 different subintervals, so n equals 6.
01:11
Delta x, to calculate delta x, that is b minus a divided by n and, um, in our case here, a and b is the limits of integration, so the 9 would be a and 27 would be b, so that'd be 27 minus 9 over, our n is 6.
01:31
So our delta x would be 27 minus 9 is 18 divided by 6 and that gives us 3.
01:37
So our delta x is 3.
01:39
So now we can use simpson's rule.
01:42
Um, the integral from 9 to 27 of f of x dx using simpson's rule, we approximately delta x over 3, so that'd be 3, what we have for delta x over 3 times, um, and now we have f of x sub 0, so x sub 0, um, i'll write that over here, um, the x, uh, x sub 0 would be the 9, x sub 1 would be 12, x sub 2 would be 15, x sub 3 would be 18, x sub 4, 21, x sub 5 would be 24, and x sub 6 would be the 27...