All right, So we're giving a political or region are other function e to the negative X square minus y squared d a, um such that the region are said to be described by the disc with the inequality of squared plus y squared is less than or equal to four on. Let's just draw up this region are really quick if we look at the boundary really quick, so extra tickets y squared is equal. Before that would just be the circles turned out the origin were afraid. Yes, to so strong this circle there 1 to 1 want. And then basically, since this inequality is less than or equal to its basically anywhere inside fetus or along to just said this would be our region are as we need to write this in polar coordinates or this interval important for corn it. So let's do that. Um, if we look at, uh, this exponent year, um, it's not a traditional X plus y squared, but we can factor out negative to make it look like a surplus of ice cream. And then we know what X squared plus y spirit does Polar cornets just r squared. So we're gonna go to that r squared negative r squared and then arj Akopian is RDR data. And now we want to think about how our data range for our think about radial lines protruding from the centre and going outwards, and we noticed that it ranges from zero to to basically the outer edge of the serval. And then it does this for 0 to 2 pi, which is our angle range or theater range. Okay. And this would be our integral that we need to sell for. Um pretty simple. Ah, what I'm gonna do first, though, is gonna notice that, uh, the inside intervals that completely are type integral and the outer and roses data a room. So with respect to the fated angle, this entire inside Enbrel is just a constant value. Because in the end, you will, um, evaluate to a new married value so we could just slide this out to the front, says hurted. Two of each and r squared times are the Are the time deserved to pie of potato? Okay, on basically, what I just did is I turned a double integral into the multiplication of two single intervals. It's pretty neat in my opinion, um, and makes it easier to solve, in my opinion to So this second, Inderal is basically just the single girl of the function one and that basically just translates always to the length of the careful. So it's just two pi, which is pretty easy. And then, for the second or the first in your girl, we actually need to use on some use substitution. We're just gonna let u equal Mega r Square are basically the supposedly function, and then or the anti derivative and its derivatives. So this will be the anti derivative, and then our would be its derivative. So we always set you to be the anti derivative, because once we drive it, get negative two r d r Then we can say RTR is equal to negative d you over to and then we can just substituted. So RDR is negative. What happened is gonna pull that 1/2 to the front. Uh, do you? Then you just want to do e to the U and then change our our limits. Say you elements. So once we plug in and serve here, we get zero. And then when we played in two, we get negative four. Um, I don't really like this. So what I do is to split them, get 1/2 in the front and said Negad 1/2 because from negative 4 to 0, usually you do you and then times two pi. So this 1/2 should just be a pie. This should be equal to each of the U. I got 40 sequel to high times we get when we played him zero, which just each Israel, which is just one and minus We get when you play, connect four so you don't get fourth, and that would be our final answer.