how to rewrite a triple integral after changing limits ? ( from dxdzdy to dydxdz ) I have the question ...

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how to rewrite a triple integral after changing limits ? ( from dxdzdy to dydxdz ) I have the question ...

Mathematics
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second question in the attached file
What is all that writing on the problem. Is that your attempt and you want us to check if it is right?
no no it's the right answer, but I don't understand how !

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I need explanation ,, my exam is tomorrow :S :S :S
1 or 2? or both?
2 only ,,
its all about translating what you got into a new direction to match the switch
is there any strategy to get the right answer ?
well, the outer one is a constant; moves from zero to it high point for starters; z = [0,4] \[\int_{0}^{4}dz\]
the middle should be in terms of the outer... so it gets a z spot right?
I think that I have always to draw ,, I think it's the only way !! but I was hopping to find simpler way ..
simpler? maybe, but i tend to only now the hard way lol
what are you studying ?
whatever I can get my hands on :)
yeah I mean simpler than drawing the graph
ive taught myself all this stuff; and as i go thru the college courses I learn ways that i was to stupid to pick up on me own
aha!! I'm suffering from my doctor in calculus this course, and I'm lost! So NOW I learned that I have to be independent specially on college,, right ?
in college *
dxdzdy dydxdz -------- -------- x: 4-2y-z y: (4-x-z)/2 x: 0 y: 0 z: 4-2y x: 4-z z: 0 x: 0 y: 2 z: 4 y: 0 z: 0 the first is a translation from point to plane x = 4-2y-z <=> y = (4-x-z)/2
the second is a translation from the seems to keep the inner one ignored x = 4-2y-z (ignore the -2y from the inner) x=4-z
same with the last? ignore the inners as 0? z = 4 -x translates to z=4
but thats just a cursory view and i aint got nuthin to prove its a general rule
maybe if we get some smarter than mes to verify or deny it :)
see if it works on double integrals maybe....
Thanks allot! I will see ...

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