Multi-variable integration with a e^u

[MasterWu77]

Homework Statement

Find the mass of the rectangular box B where B is the box determined by
0 [tex]\leq[/tex] x [tex]\leq[/tex] 1, 0 [tex]\leq[/tex] y [tex]\leq[/tex] 2, and 0 [tex]\leq[/tex] z [tex]\leq[/tex] 1, and with density function [tex]\rho[/tex] ( x, y, z ) = z e^{x+y}.

Homework Equations

"u" substitution

The Attempt at a Solution

I believe I've taken the first integral with respect to dz correctly which led me to this integral

[tex]\int[/tex] from 0 to 1 [tex]\int[/tex] from 0 to 2 (1/2)e^(x+y) dy dx

I know i need to use a "u" substitution and have u=x+y but I'm unsure of how that changes the range of the integral with respect to y. if my equation is unclear please let me know. thank you!

 

[lanedance]

write out the triple integral and use
[tex] e^{x+y} = e^x e^y [/tex]

 

[MasterWu77]

ah ok i understand how that works out! thank you! greatly appreciated!