
#1
Aug1609, 05:48 AM

P: 329

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: 26,167

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: 329

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: 329

Cheers.



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