To determine the area bounded between these two functions of this area and black here. We could go ahead and graph each of these and then notice, but the function to is on top of the blue one. And then we want to find our intersection points here. I'm here, and so you could use the graphing utility. But we'll just go ahead and do this step by him. So we'll set these two functions equal, and then we want to solve her isolate for our X here. Okay, so, um, we're gonna do a couple steps at the same time here. We're gonna, um, interchange. We're gonna multiply both sides by two. And then we're going to, uh, multiply that square root over and then square both sides. So it's gonna be this on fourth and then add the X word over. Subtract the 1/4 over. So that will give us 3/4 is equal to X squared. But then again, this will be plus or minus X or another way to say that is does the same thing as negative. Through 3/2, founded on the left and bounded on the rate positive every three over to And so really just concentrating on our set up. Now we're good to go. In terms of the integral, it's gonna be the area from Negative three. Have Route three hands the positive Route three House of the top function to minus the bottom function one over Route one buying That's expert DX. And although this looks, uh, a bit of a mess, the anti derivative of two is just to Lex, the anti derivative of the second part. There is inverse sign, and then we still have the same limits of integration. And so substituting does in and simplifying will end up with a final result of to brew three minus two. Hi, Third's. And so that is the final answer for the area under the curve and black. There, that's it.