We're going to calculate the area in close by the lips given through the equation X squared about of my X squared plus y squared B squared equals to one and Teoh calculate that we take into account. Um, the equations of the Libs is symmetric Respect to both access means that we can take only this the upper part of the lips which is defined or corresponds to Why were the Americans to Syria? In that case, Theo equation of the lease can be found solving for why in this question So why squared But be square? He's one minus x squared about about a square And so we had that. Why square is he going to be square to better, like a square times a square minus x square And then for what? Positive why we have y equals absolute body Be committed by absolute value If a times a square plus minus Sorry. Okay, times the square root off because we have taken to wearing here a square These were minus X square. And so this equation off the opera part of the leaps and and that is defined for a square minus X squared were then were able to zero, which means that X squares list done. They're going to a square. And so the absolute value of X is less than or going to the absolute value of a. But he's exists in the interval running going through and then the events of the money of a to absolute money of a then the the area enclosed by the lives. He's twice the area the area under the curve given by discretion here and these immigration the this area close with these cure the upper bar, the lease and the eggs axis is giving as the integral for a negative absolute body of a to absolute value obey Which is them in here, Off the equation, absolute value be you went about G square road off a square minus X squared differential of X, which is his question here. And so, uh, this is two times absolutely be better by absolute value, very in general, from negative after nobody obey to absolute value, obey square root of a square minus X square, the French elevates, and this internal here will be calculated using a tuna metrics institution. And for that, we're going to define implicitly a verbal filler through the equation. Mm x equal to absolutely of a sign of theater. And with that began that differential of X equal to it's absolute value, Very cold sign of the difference of theater and that we define for an angle theater in the interval negative by half by have, in order to have an inverse well, they find for these change of verbal and, um, now we can we can calculate the new limits of integration here. That's that. That's it. We're going to change the limit off integration giving this integral. So, um so we're going to say that for for X equal to negative, absolute value, very, which is the lower limits here We had that. A sign of theater is you go to and negative one, and then you have the theater is negative by half and for exit going to absolute value of a, which is the upper limit. Here we have that way have the sign of the reasonable to one so their physical to buy health, then the injured girl from negative to the value of a two absolutely of a off the square root of a square, minus X squared differential of X equal to control from negative by have to buy have of the square root of a square minus he square sign square. I'm theater times, differential of Axis subsidy value of a co sign of theater, three inch Laffita and then a sequel to the up to the body of Ray into a row from negative by half. I have. Oh, he's square root off a square times. One might assign square of the times go sign on theater differential better, and that is equal to here. The square root of a squares absolutely very time sensitive alleyway is a square dural from negative I have to buy have off the square root of on minus sine square of theater times CO sign of the French Are there at least equal to the square into row from negative by. Have to buy have here. We have absolute value of co sign Anthea Time scopes on infinity, French ill fitting, and that is a square times into world for a negative. But I have to buy health off a go sign, square off the differential thin, and this is because there is in the interval negative by half by half and there go sign, if it is possible. And so the secret to pay square integral for negative by halved by half. And these ghosts and score of there is equal to one Blasco sign of two time theater divided by two differential data on Deasy's sequel to a Square integral from negative by halved by half off. Ah, here we have to because we can get it out of the integral. On Inside we get along, plus co sign of two time theater, Fragile theater, and that is a square better by two internal from and here we were going to ride the primitive of thes function here, which is theater bless sign of 2/10 data. You better be too. And that civil waiting between developed the points negative by half and by half, and these equal to a square do anyway to at their equals by half by half, plus sign off by the by the way too minus at negative. By have we have negative. If I have minus sign off near defy everybody way too on these equal to a square to whatever two times, and we know that this is zero This is zero and we have I have a blast. I have That is, by hey square by better by two. And so remember we said at the area enclosed with the Libs is equal to here two times, Absolutely be there with absolutely of eight times the Internet we have just calculated. So you can say that the area come close but he leaves a sequel to the times. Absolute value be given in absolutely very times. These in true we calculate here is a square by health. So we have to simply five with this two and a square with absolutely a very we know that is equal to absolutely be times everybody of a times by these two body of a times absolute body be terms by And this is the area enclosed by the Libs.