Multiple Integration Question

[Playthious]

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

 

[tkhunny]

That looks possible. What have you tried?

 

[Playthious]

I tried to split it up into integral (from 0 to 1) integral (from 0 to 1) of 2x-y dxdy + integral (from -1 to 1) integral (from 1 to 2) of x^2 + y dxdy
but when I find these I don't get the right answer (31/6).
Are you not allowed to break it up like that?

 

[galactus]

You have it set up correctly. Maybe you just made a mistake in the calculations.

\(\displaystyle \underbrace{\int_{0}^{1}\int_{0}^{1}(2x-y)dxdy}_{\text{1/2}}+\underbrace{\int_{-1}^{1}\int_{1}^{2}(x^{2}+y)dxdy}_{\text{14/3}}\)

\(\displaystyle \frac{1}{2}+\frac{14}{3}=\frac{31}{6}\)