00:01
So you have the integral 4 times the sine of x dx taking between the limits of integration of pi 2 and negative pi over 2.
00:09
And you want to figure out the smallest number of intervals necessary to estimate that closely with the trapezoidal rule.
00:19
And in case you're unfamiliar with the trapezoidal rule, it just says that the integral of some function, f of x, between the upper limit b and the lower limit at a, is equal to delta x which is the difference of our two limits of integration divided by n which is a number of sub intervals times this which is f taken at the lower bound a plus two times each subsequent sub interval plus f taken at the upper limit b and if you see here, i have a plot of the function 4 times sine x on our interval, negative pi over 2, 2 pi over 2.
01:10
And you'll see that it's symmetric about the origin, right? so this area looks like it's roughly the same as this area, or even exactly the same.
01:25
Which makes me think the first thing we should try is an interval of 1.
01:31
So we can calculate delta x as b minus a, which is pi over 2, minus negative pi over 2, or just pi, which means that delta x over n is just pi over 1 or pi.
01:54
So now we can do our trapezoid rule, write in delta x over n.
02:00
And since we're only using an interval of size 1, that means we can disregard all these intermediate subintervals and just take the function at the two endpoints...