# triple integral ?

• July 14th 2013, 05:48 AM
n22
triple integral ?
Hello,
Is it bad to expand out (x+2y)² first ?then integrate it ?can doing it this lead to getting the wrong answer??
Here
∫∫∫(x+2y)²dxdydz

the first inner integral ranges from 0 to 1
the next one goes from -2 to 0
the last one goes from 0 to 3
what is the best way of integrating this ??

• July 14th 2013, 05:52 AM
Prove It
Re: triple integral ?
Yes expanding first is a valid move, and probably will make integrating the function easier as you won't have to use substitutions.
• July 14th 2013, 07:19 AM
HallsofIvy
Re: triple integral ?
And, in fact, when you do that, the integral becomes
$\int_0^3 dz\left(\int_0^1 x^2dx\int_{-3}^0 dy+ 4\int_0^1 xdx\int_{-3}^0 y dy+ 4\int_0^1 dx\int_{-3}^0 y dy\right)$

Of course $\int_a^b dx$ (or dy or dz) is just b- a.