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Let $ be the solid under the surface f(I,y) = 877 arctan(v/z) over the entire first quadrant of the zy-plane. Ifthis solid has finite volume; then its volume is V =...

Question

Let $ be the solid under the surface f(I,y) = 877 arctan(v/z) over the entire first quadrant of the zy-plane. Ifthis solid has finite volume; then its volume is V = Iosuaa where D i8 the flrat quadrant;Le. the region defined by < > and When D is an unbounded region, call Do f(5,v) 44 improper double integral: The volume under f(I,u) on D is finite ff and only if this double integral converges. (a) Write the integral Do f(I,u) dA as an improper iterated integral in Cartesian coordi- nates.

Let $ be the solid under the surface f(I,y) = 877 arctan(v/z) over the entire first quadrant of the zy-plane. Ifthis solid has finite volume; then its volume is V = Iosuaa where D i8 the flrat quadrant;Le. the region defined by < > and When D is an unbounded region, call Do f(5,v) 44 improper double integral: The volume under f(I,u) on D is finite ff and only if this double integral converges. (a) Write the integral Do f(I,u) dA as an improper iterated integral in Cartesian coordi- nates. Some ofthe endpoints of integration chould be &_



Answers

Use double integration to find the volume of each solid. The solid in the first octant bounded above by the paraboloid $z=x^{2}+3 y^{2},$ below by the plane $z=0,$ and laterally by $y=x^{2}$ and $y=x$

In the question we abuse the Dublin regulation to find the volume of the solar. The solar rebounder above the federal Lord. They're equal to one minus X squared minus y squared on above and below The X by blink Now moving forwards in the solution using the shell McCurn bigger people. Luminous indignation from 0 to 1 to buy x one minus X s where Day X is equals to buy excess whereby do minus extra part four by four limit from 0 to 1 every required by using the violent, ignorant we build a no well integration over that is you're not in next Life day by busy article for integration from minus 11 Integration from minus one minus X squared toe one minus X squared minus Texas. But I have my sweat. Do you like DX plus disorder? They never invaded. We will get immigration from minus 1 to 1 more. Upon +31 minus. That's the square and one minus six to spread the years which will finally 45 vital. And this will be the final. And from the question Thank you

In the question we have to use the devil. Integration could find the volume of this which is in the first off pain and is wanted by a parable. Life off Zen Nichols to excess with class by sweat. And this rain that exists where my square pulse Before now moving works This solution the general configuration is declared off Circle of Radius to using the shell matter integration from zero people by my lex and grew at six. Where the X it was too high. By who? By four upon by now using the double integral which is integration from zero report go integration from 04 minus x the square heads square last. Why Square day by the express dissolve in the inner integral. Really? That regulation from zero war on three and four minus X s wearing who? Excess Where? Less way less No. Yes, some sort of this We really get work on bringing one upon four x and two x two square first, two mental minus excess for less signing waas off and spy to them. It went from zero to solving this to buy, which will really find a lot. Thank you

In question were given and tempering to co I'm doesn't to. One woman is 1 to 1 for minus square. The x d. Why? It was trying to draw the figure here you were. This will function inside. Here we read the ah rub a light on. It has the high acquittal for here. It's going down here. Then we have this ago on the place. Now and then, we have considered, uh, X is innocent. Accident. Why on dizzy? And we only considered xbg minus one and one. So the minus warm is here, and ones on one is near and minus one on the other side. And why was from 0 to 1, someone's here so it would draw on the vertical line up? Yeah. So this will be the region that we're looking for here. It would be like this, Andi. It would be on the other side. Yeah. So this will be the ricin. Will it fall? Okay, so this will be the bottom. We're looking from here, so I look at it. It's kind of hard to miss. Stayed here. No, in Italy. Very. This problem will do this department. The girl. So from 0 to 1. We came the outer for now, for the inner we have extremely the variable and yeah, not just dentition is from the month 1 to 1. Therefore, here inside this one is even. And this one is also the everything is even under forward. You have the two times now we will have the entire if don't wear have been recruited. Do that is the number minutes one joint have is there to one for minus X squared minus y squared the x no. And then we get equity the rooms to 12 on the entirely rift in this one Echo Jetta for X minus. Expect to have a Jew when it's quite square. X evil it and desert you one g y. Then we get the rooms or 212 And now it will be the one inside that actually getting good. You two for minus one of the Jew minus y square. And then do you? Why? And it wasn't if I've indicative rooms that you won four months 1/2 so good you It would be, uh, with him stew as well. So it minus one. Good. You seven minus two y square do you? Why? And then we will get equal to entirely riveted this one in calculus. Want seven Y minus two Weber 3/3. Even though its energy to one didn't get Nico Judah seven minus two and three. Then we get you got your 21 minus two. So you could you 1903.

In the question We have to use the violent regulation. Find the one you off This already bonded above the parable line that s zero equals nine x squared plus y squared and below the plane Radicals to zero and they're pretty by plane acceptable +20 vicryl squid zero tactical stooping And like no moving words Dissolution volume will know different chance radicals to effects by an above The region is given by a lunatic with level integration for the region. That's why dear movie volume can Britain s double integration over the region are high Next X squared plus y squared the which can before the American as integration from zero supreme through integration from +09 sweat less vice Where Why be X indignation from zero first we will be sold in the neighbouring ticket Also keeping opening digital isn't this We will get kind of a square way less light by three and regulation from be X integration from 03 beauty next square less eight by green The yes not solving this invader They will takes x Q less pay text by three Then we went from 03 for in basically six into three with our pre blessed state and free life. The it will be for two months and this will be the final answer for the question. Thank you.


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