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.
Hi squenshl! Well, you've got the bounds, and you know how to rewrite the dV (from the Jacobian), so all you need is to rewrite x+y+z in terms of u v and w, which is … ?
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.