Here in this trouble of we have to find the volume of the solid in the first quadrant bounded by the cylinder X square plus y squared equals to four on the plane Z plus. Why is it cools to treat so they can write this equation as Z Z equals 23 minus way? No, the volume required voluble B equals to the Dublin Trickle Region are three minus way d A Are these the reason Boehner by them cylinder X squared plus y squared equals two full? Now we have a graphic These go on a graph able to find the region off integration. So let's share that after Bruno. So this is the Y axis under his exists. And this is the top view off the cell. Endo on. We have to find the volume in the first quarter totally. So I'll be concerned this area only so the volume would be equals to the double integral three minus way The day will be quilts to DX dy way. I'll be digging the horizontal strip to find the limit. So here x is, you know, on Dhere X. You know the equation of the circle is X squared plus y squared equals truthful expert big worlds too four minus y square under rude. So the upper limit would be our little four minus very square. And why the limit for wise between this line and this line? So here, why is, you know and here advice to now simply we have to integrate this double integral to find the volume regrettable because to the government dribble 0 to 2 always simplifying the inner in reverse. So let me interrogate. So it will be goes to three minus way times x on the limit is from zero to unload four minus y squared Do I A simply after plug limits. Zero to do three minus way A Parliament days on the road, full minus y squared minus zero No need to write zero because it's often no use dot de way it will be quilts to I'm just splitting the Androgel zero to do three times four minus y square Dr. D Y minus enter the zero to why times under route four, minus y squared Dr. D way. We are just all these twin Rigel Let this integral Bs I want on this integral bs I to on the value of I one minus I do would be equals two week. So first of all, I'll be simplifying the I won, so I won as equals two ventricle, zero to three. I'm taking three outside because it's a constant weaken digger outside, under route four, minus y squared Dr D Way. Now I was always a dribble by using the substitution method on I was substituting. Why is equals 2 to 70? So we can see that Do I would be equals two to society, did he? And when? Via zero b zero Saudi He has been Vaezi literally off he comes out to be a zero and when Vie is too the really off he comes out to Bs by about two So this integral will become three times limiter from zero to buy right to on Dhere Goma four square four Can Britain us to square minus vice to sign. Did that went to square sine squared? E not Did he I'm taking under a year. One more factor is there that did to co sign t daughter Didi Because devise equals two Because I did or didn t. So it will be called. I'm taking too old state on Dhere. Also, I'm taking to outside. So you get three times. Two times two is 12th zero to buy. Rightto on here will get one minus sine squared. David is a gold circle Science waiting on road. Of course. In squared, they would be called to Sainty because 90 times cause in discourse in squared B Dr D D. Now we have to use one formula. They are the consign Square D is equal to one place co sign duty divide by two. I've been using this for my hair. So you get ventricle 12 0 to pi by two one place cosigned duty divide by two dot didi and that will be called to two other times Header gummer t buy it. I'm digging slopeside so d only bless signed to be divide by two Other limits are from zero to pi by two. Now we have to simply plug the limits on Well, get the value off sick at the After plugging, the limited will get the value as six times by by two which is records to three by. So finally we have got the value of I went out. I wanted a gold stood three By now I'll be solving I do which is it quits too? White times four minus y squared dot Didi zero Toto, Harold, I'll be using a substitution method. So I was substituting Why? Square Esty? So we'll get to why do Why is it called Stoudt? And when y is equal to zero, we get these as zero I've invited schools to do we get t s full. Now I'll be blogging although values here. So I do a little big worlds too. Tentacles 0 to 4. Why did he from here? We consider it sorry. Here it is, d Why not duty? So why d y is equals to detail by two so they can write. I'm taking one by told side on Harry to come d d And here a note for minus T. Now we have to just simplify this integral which is equal to one by two Onda The trigger of this would be four minus two to the power three by two Divide by everybody do over again right to buy three on the limits are and read one negative sane because there's my next easier. So the limiters from 0 to 4 not just simply have to plug the limits and after plugging elements, will get the value s eight by three. So finally, volume what we calls to I one minus I too. And I want we have all planned out tree by minus. I do is eight by tree which will be equal to 6.758 So finally the required volume is V equals to 6.758 This is a final answer.