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

Question

nice · Answer

second question in the attached file

anonymous · Answer

What is all that writing on the problem. Is that your attempt and you want us to check if it is right?

nice · Answer

no no it's the right answer, but I don't understand how !

nice · Answer

I need explanation ,, my exam is tomorrow :S :S :S

amistre64 · Answer

1 or 2? or both?

nice · Answer

2 only ,,

amistre64 · Answer

its all about translating what you got into a new direction to match the switch

nice · Answer

is there any strategy to get the right answer ?

amistre64 · Answer

well, the outer one is a constant; moves from zero to it high point for starters; z = [0,4]

$$\int_{0}^{4}dz$$

amistre64 · Answer

the middle should be in terms of the outer... so it gets a z spot right?

nice · Answer

I think that I have always to draw ,, I think it's the only way !! 
but I was hopping to find simpler way ..

amistre64 · Answer

simpler? maybe, but i tend to only now the hard way lol

nice · Answer

what are you studying ?

amistre64 · Answer

whatever I can get my hands on :)

nice · Answer

yeah I mean simpler than drawing the graph

amistre64 · Answer

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

nice · Answer

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 ?

nice · Answer

in college *

amistre64 · Answer

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

amistre64 · Answer

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

amistre64 · Answer

same with the last? ignore the inners as 0?

z = 4 -x  translates to z=4

amistre64 · Answer

but thats just a cursory view and i aint got nuthin to prove its a general rule

amistre64 · Answer

maybe if we get some smarter than mes to verify or deny it :)

amistre64 · Answer

see if it works on double integrals maybe....

nice · Answer

Thanks allot! I will see ...