1. Multiple Integration

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

2. Decompose:

$\displaystyle\iint_{B_1\cup B_2}f(x,y)dxdy=\displaystyle\iint_{B_1}(2x-y)dxdy+\displaystyle\iint_{B_2}(x^2+y)dxdy$

Regards.

Fernando Revilla

3. Start by drawing the two sets on a graph. It should be easy to see that $B_1$ and $B_2$ overlap only on the boundaries so the integral over both is just the sum of the integrals over each, as Fernando Revilla says.

4. Originally Posted by HallsofIvy
$B_1$ and $B_2$ overlap only on the boundaries so the integral over both is just the sum of the integrals over each, as Fernando Revilla says.
Of course is important your comennt ( $\mu (B_1\cap B_2)=0$ ) .

Regards.

Fernando Revilla