# Suitable change of variables for this triple integral?

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• May 18th 2011, 03:47 AM
LHS
Suitable change of variables for this triple integral?
http://img542.imageshack.us/img542/5600/unledsn.png

Can anyone help me with coming up with a suitable change of variables for this triple integral? (last part of question)
having trouble getting spherical polars to work, if anyone has any other suggestions it would be great!

this is from here, not a take home test
Course Material for Calculus in Three Dimensions and Applications | Mathematical Institute - University of Oxford
sheet 3
• May 18th 2011, 04:37 AM
FernandoRevilla
Hint Use the Spectral Theorem for the corresponding quadratic form and apply the substitution \$\displaystyle (x,y,z)^t=P(u,v,w)^t\$ with \$\displaystyle P\$ orthogonal such that \$\displaystyle P^{-1}AP=D\$ (D diagonal) .
• May 18th 2011, 04:43 AM
LHS
Yeah.. thanks, but as that's not in my first year course the questions i'm facing aren't really geared towards that approach, it would probably be better for me to understand how they want me to do it
Thanks you though :)
• May 18th 2011, 07:12 AM
FernandoRevilla
Quote:

Originally Posted by LHS
Yeah.. thanks, but as that's not in my first year course the questions i'm facing aren't really geared towards that approach, it would probably be better for me to understand how they want me to do it
Thanks you though :)

Haven't you studied a previous Linear Algebra course?