Consider the rectangles
B1 defined by 0< x <=1, 0<=y<=1
B2 defined by 1<=x<=2, -1<=y<=1
and the function
f(x,y) = { 2x -y if x< 1
{ x^2 + y if x>=1
Compute integral (B1 U B2) of f(x,y)dxdy
Decompose:
$\displaystyle \displaystyle\iint_{B_1\cup B_2}f(x,y)dxdy=\displaystyle\iint_{B_1}(2x-y)dxdy+\displaystyle\iint_{B_2}(x^2+y)dxdy$
Regards.
Fernando Revilla
Of course is important your comennt ( $\displaystyle \mu (B_1\cap B_2)=0$ ) .
Regards.
Fernando Revilla