Register to reply 
Change of variableby squenshl
Tags: variable 
Share this thread: 
#1
Aug1609, 05:48 AM

P: 328

How do I evaluate the triple integral [tex]\int\int\int_G[/tex] x+y+z dV using a suitable change of variable where G is the region
0 [tex]\leq[/tex] x+y [tex]\leq[/tex] 1, 2 [tex]\leq[/tex] y+z [tex]\leq[/tex] 3, 4 [tex]\leq[/tex] x+z [tex]\leq[/tex] 5. I know to let u = x+y, v = y+z, w = x+z and I end up with the det(jac) = 2 [tex]\Rightarrow[/tex] 1/det(jac) = 1/2. But I'm stuck after that. Help. 


#2
Aug1609, 09:26 AM

Sci Advisor
HW Helper
Thanks
P: 26,148

Hi squenshl!



#3
Aug1609, 12:59 PM

Sci Advisor
HW Helper
PF Gold
P: 12,016

Hint:
What does u+v+w equal, in terms of x+y+z? 


#4
Aug1609, 05:07 PM

P: 328

Change of variable
u+v+w = 2x+2y+2z = 2(x+y+z),
[tex]\Rightarrow[/tex] x+y+z = (u+v+w)/2. Then just chuck that in. Is that right. Thanks. 


#6
Aug1709, 05:20 PM

P: 328

Cheers.



Register to reply 
Related Discussions  
Variable Change... what?!  General Math  8  
PDE  Change of variable  Differential Equations  4  
A change of variable  Introductory Physics Homework  4  
Change fo variable 2  Introductory Physics Homework  0  
Change of variable...  Calculus  1 