00:01
All right, in your question, you're supposed to use the trapezoidal rule with n equals 6 to determine or estimate the area under this curve.
00:08
Now, the trapezoidal rule is usually written out as delta x over 2 times f of x sub 1 plus 2 times f of x sub 3 plus dot dot dot dot 2 times f of x sub n minus 1 plus f of x sub n sub n now that's typically what the formula looks like how do we calculate delta x delta x is b minus a divided by n so for your question your b values the end of the interval which would be 6 minus a would be the beginning of the end of the interval interval, which is 0, divided by n, which is 6.
01:08
So for you, your delta x is 1.
01:12
So we're going to have one half times.
01:15
Now, f of x is the value of the function at the first x value in the interval.
01:21
So that would be 3.
01:24
That's our first height right here.
01:27
Your second one, it was going to be 2 times f of x2, and that's at 5.
01:35
Now, what's going on here? before i go, any further is we're calculating the area of a trapezoid.
01:42
This is our first trapezoid.
01:44
And the way you calculate that is the height divided by two, which our height is the distance between these two parallel sides, and we know that's one.
01:55
Your b1 would be three, and your b2 is five.
02:02
So that's what's going on, but why do we have two times this one and don't have two times this one.
02:09
The reason we have two times that second one and all the ones in the middle is because those numbers are going to get counted twice when we do the next trapezoid.
02:20
So we would have this value counted twice, this value counted twice, and so on.
02:28
So hopefully that helps you understand a little bit about where the trapezoidal rule comes from.
02:33
And now i can just complete this process, working down the line.
02:39
The next one would be two times four...