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

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- Nov 18th 2010, 04:45 PMPlaythiousMultiple 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 - Nov 18th 2010, 11:52 PMFernandoRevilla
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 - Nov 19th 2010, 03:00 AMHallsofIvy
Start by drawing the two sets on a graph. It should be easy to see that $\displaystyle B_1$ and $\displaystyle B_2$ overlap only on the boundaries so the integral over both is just the sum of the integrals over each, as Fernando Revilla says.

- Nov 19th 2010, 03:13 AMFernandoRevilla
Of course is important your comennt ( $\displaystyle \mu (B_1\cap B_2)=0$ ) .

Regards.

Fernando Revilla