00:01
Here i'll review the idea of a remand sum.
00:05
Remon sum is an approximation for the area under a curve using rectangles.
00:12
So we're trying to do the same thing that an integral of that function would do, except we are approximating the integral.
00:22
So the remand sum is basically, you usually want to divide the interval into even pieces.
00:31
So we're going to take the endpoints b and a and divide them by sum number n.
00:44
So we're going to make n rectangles.
00:48
Then we are going to sum over the area of each rectangle by taking the base as the delta x and the height as the function evaluated at some one of the end points.
01:07
Of the rectangle.
01:13
Ok, so this gives an approximation of the area under the curve f of x by using sub -intervals that are rectangles.
01:33
And i'll just kind of sketch that as we get into the example.
01:37
So the example we're going to do is the integral of 3 sine of x dx from 0 to pi.
01:44
It kind of looks like the graph above, maybe not perfectly, but it maxes out at 3 and looks fairly symmetric about that middle point.
02:08
So we're going to use what are called left end points and divide into n equals four rectangles.
02:18
So we can already start with delta x is equal to pi minus zero over four, or pi over four.
02:36
And i can show that on the diagram.
02:40
Let's see, i hope i've drawn this in a way that makes some sense.
03:01
Yeah, one, two.
03:04
Okay, i think i got that.
03:06
So here we have zero.
03:08
The next data point is pi over four, then pi over two, three -fourths pi.
03:16
And finally, pi.
03:20
So what we're going to do is draw the rectangles.
03:22
The first rectangle has a height of zero...