00:01
So the first thing that i would do is since we need six sub -intervals, i'm thinking about how to get from 1, from 0 to 1, i should say, divided by 6.
00:09
Well, that gives me 1 -6.
00:11
So what i would do is make a chart then, starting at x and figuring out what sign of pi -x is.
00:21
Starting at 0, well, sine of 0 is 0.
00:25
But then as you do intervals of one six, well then, i'm assuming they want equal sub -intervals, well, sine of pi over six is equal to one -half.
00:37
And then the next one, i'm just going to leave it as two -six.
00:40
Well, i could write it, that's one -third, because sine of pi over three is root three over two.
00:46
And then the next one would be three -six, which is one -half, and sine of pi over two is one.
00:53
And then we're back to, i'll just write two -thirds.
00:56
Is also root 3 over 2.
00:59
And then sign of 5, pi over 6 is 1 half again.
01:07
And then if you get to 1, sign of pi is back to 0.
01:12
So what we have going on, i don't mind drawing a graph just because it might be helpful, is our graph looks like this on the interval from 0 to 1.
01:21
And i have 1, 2, 3, 4, 5, 6 intervals.
01:27
And what we're really having happening here is we're making a trapezoid that looks like this.
01:33
And then your next trapezoid looks like this.
01:36
And then the next trapezoid looks like this.
01:41
I'm trying to draw it pretty nice, but i don't know if i'm doing it justice.
01:45
But if you think about the area of a trapezoid, it's equal to one -half times the height times the bases.
01:54
Now you have to be careful here because the bases are actually the up and down ones and the height is along this side.
02:01
Now, each one of these heights or widths are going to be one -six...