00:01
We want to integrate x minus y quantity squared over this region defined by bounded by y equals x, y equals 2, and x equals 0.
00:16
So we write that in set notation.
00:18
Y goes from, y goes from x to 2, and x goes from 0 to 2.
00:28
So we can write out the integral, and again we can, this should be an easy integral for you to do at this point.
00:35
So i'm not going to go over the details of it, but we wind up with four thirds.
00:42
And here's the region.
00:43
They didn't tell us we didn't need to plot that, but you can see it's kind of, it's parabolic kind of, and that's, you know, a line of zeros when x equals y here.
00:52
And we can see here, if we look at him that this cube is 2 by 4 by 2, so 16.
00:59
That would have be having units, a volume of 16 cubic somethings...