00:01
For this problem, we have been given a double integral and a region r, which is a rectangular region.
00:07
And we've been asked to sketch the solid that falls between that rectangle r and the curve.
00:13
We're not going to actually find it numerically.
00:15
We're just going to try to sketch it.
00:17
So let's see what we can tell here.
00:21
First of all, i'm going to give myself three dimensions here.
00:24
I've got x, y, and z.
00:30
And i'm going to apologize in advance.
00:33
I'm a math person, not an artist, so three -dimensional things, especially trying to do it here on this whiteboard is a little tough, but i'll try to describe it as best i can and do my best stab at the actual picture.
00:45
Okay, let's take a look first at our curve.
00:50
The square root of 9 minus y squared, and that's going to be our, that's our z.
00:56
Now, there is no x here.
00:58
So that tells me that x is not going to play a part.
01:00
Whatever this is, it's going to, it's going to.
01:02
Going to be the same wherever i go along the x -axis.
01:06
So let's take a look at how z and y relate to each other.
01:09
I'm going to get rid of that square root.
01:11
So i'm going to square things and put my variables on the same side.
01:16
Y -squared plus z squared equals nine.
01:19
Well, this is a circle.
01:21
Y -square plus z -square...