00:01
Okay, so we need to find a triple integral to find the volume of this solid.
00:06
Well, as you can see we're given, we need to first figure out what the region is.
00:12
The region, so we've already given values for, the region values for x and y and note that if you look at the region on graph, it goes between 0, z is always bounded by 0 and the graph of a function.
00:34
So the height is the graph of the function, so it's 2xy.
00:40
Okay, so this is the region and we want to find the volume of this region.
00:44
So to find the volume of this region with a triple integral is to take a triple integral and then just integrate 1dv.
00:54
And now let's, so we've already written how to parametrize this region.
00:59
X is between 0 and 2, y is between 0 and 2 and then z goes between 0 and 2xy.
01:08
1dz dy dx.
01:13
So this is the integral we need to solve...