00:01
So we want to go over how to calculate the riemann sum.
00:06
We're going to start off with f of x equals 52x minus 13 over the interval from 0 to 2, or n is equal to 4.
00:17
So the first thing we want to do when we're finding remand sums is we want to find the delta x.
00:22
What we know delta x is b minus a over n, which means it's 2 minus 0 over 4, which gives us a 1⁄2.
00:30
Now that we found that, we want to set up the left -hand sum.
00:36
So that's going to equal delta x times we want to start with the leftmost value.
00:43
So f of zero.
00:44
And then we want to increment it by our delta x, one -half.
00:46
So f of one -half plus f -of -1.
00:51
And then we want to go up to four of these.
00:54
So we're going to plus f of one and a half or f of three halves.
00:57
So now we have one, two, three, four.
01:00
And that is going to be how we set up the sum.
01:03
So now we want to add this all up.
01:09
So again, this is going to be f of x equaling 52x minus 13.
01:18
And then we're going to have our delta x times f of zero plus f of one -a -half plus f of one plus f of three -half.
01:41
And our delta x in this case is going to be so we end up getting our left hand sum to equal 52.
01:49
Well now let's do this and we can even speed up the process possibly for the other ones.
01:56
So in this case we want to do a left hand sum for this integral.
02:03
We're going f of x equals 3x squared plus 1 over the interval from 2 to 18.
02:12
Or n equals 4.
02:16
So in this case, our delta x equals 18 minus 2 over 4, so that's going to be 16 over 4, which is 4.
02:24
So we want 4 times f of 2 plus f of 6 plus f of 10 plus f of 14.
02:38
That's the left -hand sum...