# Help with simplifying integral

1. Nov 27, 2011

### xnitexlitex

1. The problem statement, all variables and given/known data
We need to solve the double integral:

6 -2/3x+4
∫ ∫ [12-2x-(3y/4)] dy dx
0 0

2. Relevant equations
(a+b)2 = a2 + 2ab + b2

3. The attempt at a solution
I've got to:

6
(1/4) ∫ [12y-2xy-(3y2/2)] evaluated at -2/3x + 4 and 0.
0
6
(1/4) ∫ [12(-2/3x + 4) - 2x(-2/3x + 4) - (3(-2/3x + 4)2/2)]
0

This is where I'm stuck. I could solve the rest of the integral if I could simplify this right. Sometimes, I think simplifying the integral is harder than the integration itself.

2. Nov 27, 2011

### ArcanaNoir

This isn't right.Where did the 1/4 come from? And it's not (3y2/2), it's 3y2/8.
Which, (1/4)(3/2)=(3/8), but then the other terms are wrong, because (1/4)12= 3, and it's not 3y.