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Sketch the region enclosed by the given curves and find its area.

$ x = 2y^2 $ , $ x = 4 + y^2 $

$\frac{32}{3}$

Applications of Integration

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Baylor University

University of Michigan - Ann Arbor

Idaho State University

right. Let's sketch the region. Close it there by those to curb serves Hurst So very sour X Y claim And now actually goes to Eco's Tu tu y Square. So it's a problem open to the right. Looks like there's this is r X because Teo who I square and the second one also a problem is, um X equals two or plus why square So he's also open to the open to the right soon. Here is for since the coefficient is ones that off too, which means there's first curve. You catch up with the second curve, so they will have a intersection. This is right. Oh, Cindy Intersection. Even her sect here. And there's this symmetric ex access. All right, so eventually we will get this one ship in closed area. Okay, um and, uh, they observed that everything's represented by why? Um, it's like Weiss or independent variable here. So on to find this area really take the integral integral with respect. Why? Okay, so then we need to find a boundary for wire. And as you see, there's, uh I call this one. This is our way too. Her business are my one. This is star like Tio of the intersection Point the one hungry Find this by y y Teo. Basically, we just plugging those two functions. You know, this intersection happens when two y square eco's to four plus twice where that we can solve this. Um, you know, this is then why you coast too Remove this y squared to the other side So we got one white square you goes for I get why he goes to positive or negative too, though, since our wise next year So I want their yuko's inactive too, You know, a way to Mary close to positive too. So are you. Grover goes from neck to to to to and the thing inside. And you could always just to the right curve minus left curve. So are right. Pervy theories for plus y square Linus or left curve are left curvy. So our left curve use on to y square. Okay, so they played pieces just four minus y square. An interview ity for four minus bye Squares for why minors? Thank you. Third it like you. Me very hungry by close to two. And why he goes connected to Okay, So this who he chose Teo. The first one is eight miners, eight over three miners, back to eight class, you know. Or three. What? So this is very close to thirty two cor three.