00:01
We need to approximate the integral from 0 to 7 of the square root of 49 minus x squared using the trapezoid rule and n equals 8.
00:17
So if we're using the trapezoid rule, we first need to find delta x.
00:31
Delta x is equal to 7 minus 0 over 8.
00:38
So that is 7 eighths.
00:43
So that means we have the end points, 0, 7 eighths, 7 quarters, 218s, 7 -8s, 7 -8s, 7 -8s, 7 -5s.
00:57
So you're just adding 7 -8s each time.
01:00
35 -8s, 21 quarters, 49 -8s, and 7.
01:13
So we can move these down.
01:19
And this is x and we'll find f of x.
01:25
This is x and we'll find f of x.
01:31
So we want actually two times f of x for the trapezoid rule.
01:41
So here two times f of x when x is 0, this is 7.
01:55
I'm going to write this in red because this is just f of x.
01:59
Our first endpoint is one times and then every other endpoint is two times to get the trapezoid rule.
02:08
So this is 13 .89.
02:15
For seven quarters, it is 13 .56.
02:22
For 21 eighths, it's 12 .98...