00:01
Okay, so we'd like to evaluate this, a new rule of 5 minus xda over the region r using a volume.
00:12
So, r is just a region from 0 to 5 in x and 0 to 3 in y.
00:19
So it's just this, it's just a first quadrant rectangle like this.
00:28
So this is x, y, and then this goes to five.
00:34
This is the origin, and then here's y equals three.
00:39
So our region is just this five by three rectangle.
00:46
So then now that we know our region, we'd like to know what our integral is, or integrand.
00:54
So with this as an integral of a function, of x and y, the a, we know that our function of x and y is just 5 minus x.
01:07
So this graph, when you graph this in 3d space, this is x, y, and z, say this is equal to z.
01:23
So the graph z equals 5 minus x describes a plane that only changes.
01:31
An x so if we look at x equal 0 it should be at z equals 5 and x equals 5 it should be at z equals 0 so our our plane is something like this so this is one edge and then this is our plane so to get a better view we we can just draw it through the xy plane.
02:10
So, i mean the xx plane.
02:13
So if we draw this into just the xx plane, so something like this, the xx plane, it's just a line like this...