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 $$\leq$$ x $$\leq$$ 1, 0 $$\leq$$ y $$\leq$$ 2, and 0 $$\leq$$ z $$\leq$$ 1, and with density function $$\rho$$ ( 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

$$\int$$ from 0 to 1 $$\int$$ 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
$$e^{x+y} = e^x e^y$$

 

[MasterWu77]

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