Triple integral q
How are we meant to sketch with just the information of z? By that inequality I can see that z>=0 and |y|<=1-|x|(which is like a diamond) but what about the region of x?
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Original post by cooldudeman
How are we meant to sketch with just the information of z? By that inequality I can see that z>=0 and |y|<=1-|x|(which is like a diamond) but what about the region of x?
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It is a pyramid!
Original post by TeeEm
It is a pyramid!
How did u just know that?
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Original post by cooldudeman
let x>0, y>0
then this is the plane z=1-x-y or x+y+z=1
draw a 3D set of axis and plot x=1, y=1, z=1
join them into a triangle
the volum is under that since z>0
but surface is even in x and in y (mods)
so it is the same above all four quadrants!
Any good?
Original post by TeeEm
let x>0, y>0
then this is the plane z=1-x-y or x+y+z=1
draw a 3D set of axis and plot x=1, y=1, z=1
join them into a triangle
the volum is under that since z>0
but surface is even in x and in y (mods)
so it is the same above all four quadrants!
Any good?
then this is the plane z=1-x-y or x+y+z=1
draw a 3D set of axis and plot x=1, y=1, z=1
join them into a triangle
the volum is under that since z>0
but surface is even in x and in y (mods)
so it is the same above all four quadrants!
Any good?
To be completely honest, no I still dont get it......
Just curious would -1<=x<=1 be the bound for x when doing the triple integral?
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Original post by cooldudeman
To be completely honest, no I still dont get it......
Just curious would -1<=x<=1 be the bound for x when doing the triple integral?
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Just curious would -1<=x<=1 be the bound for x when doing the triple integral?
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No
z: 0 to 1-x-y
y: 0 to 1-x
x: 0 to 1
the answer need to be multiplied by 4 at the end
Original post by TeeEm
CORRECTION NOT x4
? it actually made sense when you said multiply by 4 at the end. so you don't?
Original post by cooldudeman
? it actually made sense when you said multiply by 4 at the end. so you don't?
no because of the xy bit in the integrand
it is the same in the 1st and third quadrant xy (-x)(-y)
the same in 2nd and 4th (-x)(y) and (x)(-y)
I am trying to do the question now properly
Original post by TeeEm
no because of the xy bit in the integrand
it is the same in the 1st and third quadrant xy (-x)(-y)
the same in 2nd and 4th (-x)(y) and (x)(-y)
I am trying to do the question now properly
it is the same in the 1st and third quadrant xy (-x)(-y)
the same in 2nd and 4th (-x)(y) and (x)(-y)
I am trying to do the question now properly
OK please lemmi know how it goes because I am very confused
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Original post by cooldudeman
30 min approx cause I am doing a neat solution for myself too ...
(I steal you see ....
)Original post by TeeEm
30 min approx cause I am doing a neat solution for myself too ...
(I steal you see ....)
(I steal you see ....
)Lol no problem!
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Original post by cooldudeman
I have done 1/4 of the question! (very long and very messy). I think is correct.
Proof read for me please and I am sure there are symmetries in this problem but they are TRICKY.
I need clear head before I add to my model solution otherwise I will have to redo and this takes ages.
send email
Original post by TeeEm
I have done 1/4 of the question! (very long and very messy). I think is correct.
Proof read for me please and I am sure there are symmetries in this problem but they are TRICKY.
I need clear head before I add to my model solution otherwise I will have to redo and this takes ages.
send email
Proof read for me please and I am sure there are symmetries in this problem but they are TRICKY.
I need clear head before I add to my model solution otherwise I will have to redo and this takes ages.
send email
Ill PM u
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Original post by cooldudeman
thanks
Original post by TeeEm
no because of the xy bit in the integrand
it is the same in the 1st and third quadrant xy (-x)(-y)
the same in 2nd and 4th (-x)(y) and (x)(-y)
I am trying to do the question now properly
it is the same in the 1st and third quadrant xy (-x)(-y)
the same in 2nd and 4th (-x)(y) and (x)(-y)
I am trying to do the question now properly
I figured out how to sketch it. I considered 4 cases, x,y>0, x,y<0, x>0,y<0, and x<0,y>0. And they all give quarter of a prisim so I don't get why you don't multiply by 4 after finding the volume for the positive xyz quadrant. It'd make perfect sense...
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Original post by cooldudeman
glad it made sense
Original post by cooldudeman
I figured out how to sketch it. I considered 4 cases, x,y>0, x,y<0, x>0,y<0, and x<0,y>0. And they all give quarter of a prisim so I don't get why you don't multiply by 4 after finding the volume for the positive xyz quadrant. It'd make perfect sense...
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There is symmetry but I cannot justify/see it.
The integral gives 1/40 over the 1st and 3rd quadrant and 1/120 over the 2nd and the 4th quadrant.
Nightmare Question
Original post by TeeEm
There is symmetry but I cannot justify/see it.
The integral gives 1/40 over the 1st and 3rd quadrant and 1/120 over the 2nd and the 4th quadrant.
Nightmare Question
The integral gives 1/40 over the 1st and 3rd quadrant and 1/120 over the 2nd and the 4th quadrant.
Nightmare Question
Yeah I just realised that a pyramid is not all equal when split into four parts by the corners. So the answer is 1/40+1/40+1/120+1/120? Also are you gonna do a full solution to this in the next couple of days? I know you're busy so dont take that question as me being rude lol.
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