All right. We want to find the area inside the cardio. I'd articles one plus coastline data, but outside the circle R equals three coastline data. So here's what articles one plus coastline data looks like in rectangular. So we'll use that to get the picture in. Polar. It's at zero degrees were at two at five or two were at one. And by the time we get to pie, we're back. We're at zero and all in a positive way. And then the same thing on the other part. Okay, that's pretty good. What colored in? All right. And then articles three Coastline thing that looks like this at zero degrees, we're at 3123 and then at pi over to work to zero and then back again, Pretend like that's a circle. So we went inside the cardio it but outside the circle. So this green part right here. Okay, so it's easy to see that we're going from the cardio oId to to the, um, circles. So from the card oId to the circle, our it goes three coasting data R d r d theta. So the interesting problem here is what angles are these from where to? Where should we go? So we need to set the two equations equal to each other, since they're both equal that are so one plus cosine theta equals three cosine theta. So one equals to cosign. Data go. Xanterra equals one half. So coastline 30 equals one half, one half square 23 That's 60 degrees, or pi over three. So let's call this one minus 60. And this one positive 60 or minus pi over three two pi over three. So that's the integral. All right, so first integration gives us our squared over two. So let's put one half once by over 3 to 5 or three r squared from one plus coastline data to three coastline data geetha. Right now. Okay, so it's one half in a grove minus pi. Over 3 to 5 or three. Nine. Cosine squared. Data minus one plus to cosign data plus coastline square data the photo. So one half minus five or 3 to 5 or three. Eight. Coastline squared. Data minus two. Cosine theta minus one. Did they know? Okay, so we're gonna put in an identity for that coastline squared. So I got one half when It's Piper 32 pi over three. Eight times one plus cosine. Tooth data over to when is to cosign theta minus one. Uh, data. I'm starting to really go sideways here. Okay, so see if I can straighten out to one half minus pi over 3 to 5 or three. So we have eight times a half, which is four for minus one three minus plus eight over to which is four. So four cosign tooth data minus two. Cosine theta d theta. Now I'm ready to integrate. Still going sideways. One half. What website back in here. One half, three fada plus to sign to theta minus two sine theta from minus pi. Over 32 pi over three. All right. Okay. We're gonna We're gonna need all four of them, so let's just put him in here. Square to three. It's where 23 minus the square to three. Minus the square to three. So I have one half. Three times five or three. So pi. Plus two times the sign of two pi over three, which is square to three over to minus two. Signed pi over three, which is squared of three over to minus parentheses. E three times minus pi over three, plus two times the sign of minus two. Power three screw three over. Two minus two times. This one. All right, so now we have one half pi plus pi. So two pi two squares of 3/2, minus two squares. Three over to those canceled minus. Plus those canceled E get pie for the answer.