anonymous
  • anonymous
find the volume of the domain D: x^2+y^2≤2z ; 0≤z≤2
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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ChillOut
  • ChillOut
What kind of surface do you have?
ChillOut
  • ChillOut
\[\frac{x²}{a²}+\frac{y²}{b}= \frac{z}{c}\] What kind of surface is this?
ChillOut
  • ChillOut
I mean, over b²

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anonymous
  • anonymous
i dont know. i don't remember the formula. i've done this 3 years ago :)
ChillOut
  • ChillOut
It's a paraboloid... You can use double integrals so solve this. It intersects the plane z=2
ChillOut
  • ChillOut
Do you know how to do it?
ChillOut
  • ChillOut
I mean, the plane z = 4
anonymous
  • anonymous
why a double and not a triple integral? \[\int\limits \int\limits \int\limits f(x,y,z) dxdydz\]
ChillOut
  • ChillOut
Just a moment, doing it on paper.
anonymous
  • anonymous
http://clip2net.com/s/5efeON here is a print screen of a similar example. but i dont now what f i have here
ChillOut
  • ChillOut
Indeed it is supposed to be a triple integral. But it simplifies to a double one. Just one more moment...
ChillOut
  • ChillOut
Do you have the answer?
anonymous
  • anonymous
no. it's the subject from last year exam.
dan815
  • dan815
want help?
anonymous
  • anonymous
yes please :(
dan815
  • dan815
or u done?
dan815
  • dan815
ok
dan815
  • dan815
lets start by drawing
dan815
  • dan815
x^2+y^2≤2z z>x^2+y^2/2
dan815
  • dan815
|dw:1371220521885:dw|
dan815
  • dan815
so what is the intersection circle look like on that plane?
dan815
  • dan815
|dw:1371220558399:dw|
anonymous
  • anonymous
elipse?
dan815
  • dan815
u know it will intersect the plane at z=2 so sub it in and tell me the equation of the circle there
dan815
  • dan815
where are u getting ellipse from
dan815
  • dan815
x^2+y^2 =2z; where z = 2 x^2+y^2 =4 so a circle with radius 2
dan815
  • dan815
|dw:1371220774430:dw|
dan815
  • dan815
now u know the shadow this volume casts on the xy plane let us integrate
dan815
  • dan815
|dw:1371220851687:dw|
dan815
  • dan815
and best if we switch this to polar coordinates for convenience
dan815
  • dan815
|dw:1371220905575:dw|
dan815
  • dan815
got it?
anonymous
  • anonymous
yes thanks
anonymous
  • anonymous
decent work dan815
dan815
  • dan815
bhHhHaahaha
dan815
  • dan815
integrals are my *****
anonymous
  • anonymous
ahahahaha
anonymous
  • anonymous
thats a good movie to watch starring dan. lol integrals are my ****
anonymous
  • anonymous
id go pay money to see that
dan815
  • dan815
hahaha
dan815
  • dan815
ill open with that famous line i made up about the woman in the shadows called wisdom
dan815
  • dan815
lmao
anonymous
  • anonymous
hahahaha
anonymous
  • anonymous
god. i gotta hit the sack now. getting late.

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