00:01
In this question, we want to find the volume of the region that's bounded above by the paraboloid z equals 3x squared plus 2y squared and below by the square r.
00:10
R is the set of x values that range from negative 2 to 2 and y ranges from negative 2 to 2 as well.
00:18
And so we're going to compute a double integral, the double integral of my paraboloid, the double integral of 3x squared plus 2y squared.
00:30
And i'll do this in the dx dy order, but it doesn't really matter.
00:36
You see my x's this time, they range from negative 2 to 2, while my y's, they range from negative 2 to 2 as well.
00:46
So now i need my antiderivative with respect to x.
00:50
So my antiderivative with respect to x is going to be 3x cubed over 3 x cubed plus 2y squared x.
01:03
And this gets evaluated from negative 2 to 2 dy.
01:10
So let's see, i'm going to plug in my top limit of integration.
01:14
I plug in the 2.
01:16
When i do, i get 8 plus 2y squared times 2, that's 4y squared.
01:24
And from this, i subtract what i get when i plug in negative 2.
01:30
When i plug in negative 2, what do i get? i get negative 2 being cubed, that's negative 8.
01:37
And then i get 2y squared times negative 2, that's negative 4y squared, all of this dy...