00:01
With all the double integrals here, we're going to start by integrating the inside first.
00:05
So this is with respect to x.
00:08
So then we're going to treat y as a constant.
00:11
So integrating 3x, we'll get 3x squared, all divided by 2 plus y, times x, because the integral of a constant is that multiplied by its variable.
00:27
And then we're going to integrate this from negative 2 to negative 1.
00:32
All of this is still within the brackets here.
00:38
We still have the integral on the outside.
00:41
So eventually, once we get an answer on the brackets on the green, we're going to have to integrate that answer with respect to y.
00:49
So then now plugging in here, we're going to end up with plugging negative 1 in.
00:55
It's going to give us three halves and then minus y.
01:04
Then all of that subtract, negative 2n, rather, squared 4, divided by 2 is 2, 2 times 3, 6, and then minus plug 2 in for x, negative 2n for x.
01:19
That's negative 2y.
01:23
So then all of this, we could just go ahead and simplify this first.
01:27
So let me just rewrite that.
01:29
That's the same thing as negative 9 halves.
01:34
And then it becomes plus y, because we have positive 2y on the right with distributing the negative.
01:41
So that's plus y...