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Multi-variable integration with a e^u

  1. Oct 20, 2009 #1
    1. The problem statement, all variables and given/known data

    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}.

    2. Relevant equations

    "u" substitution

    3. 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!
  2. jcsd
  3. Oct 21, 2009 #2


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    Homework Helper

    write out the triple integral and use
    [tex] e^{x+y} = e^x e^y [/tex]
  4. Oct 21, 2009 #3
    ah ok i understand how that works out! thank you! greatly appreciated!
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