Confined Volume Calculation: How to Determine the Volume Within a Given Surface?

[supercali]

Homework Statement

calculate the volume confined within this surface
$$\left( x+y+z \right) ^{2}+ \left( 2\,x+y+z \right) ^{2}+ \left( 3\,x+<br /> 4\,y+z \right) ^{2}=4$$

Homework Equations

The Attempt at a Solution

i know that i need to use different variables but i just can't make it

 

[Dick]

What choice of coordinates will turn that into a sphere u^2+v^2+w^2=4??

 

[supercali]

What choice of coordinates will turn that into a sphere u^2+v^2+w^2=4??

even if i do choose
u=x+y+z
v=2x+y+z
w=3x+4y+z

which jacobian will i use?
because i need to use another transformation to spheerical coord...

 

[supercali]

never mind got iy thanks allot for the hint