In a plane there is a triangle B described by the properties: x

Question

In a plane there is a triangle B described by the properties: x<=2, y<=2, x+y>=2.
Calculate the double integral.
I can plot it but somehow I get a negative result.

anonymous · Answer

are we finding area or volume?

anonymous · Answer

volume

anonymous · Answer

then we need a function to integrate over given region

anonymous · Answer

oh, I'm sorry...I forgot half of the question

anonymous · Answer

the function that needs to be integrated is 2x-3y

anonymous · Answer

do you mean, what I calculated?

anonymous · Answer

Hold on

anonymous · Answer

$$x <= 2 $$ $$y <= 2 $$ $$x + y >= 2$$ $$y >= -x + 2$$

anonymous · Answer

http://www.wolframalpha.com/input/?i=y+%3E%3D+-x+%2B+2%2Cx%3C%3D2%2Cy%3C%3D2

anonymous · Answer

That's was wrong
$$\int _0^2\int _{2-x}^22 x-3y dydx$$

anonymous · Answer

so the outer integral goes from 0 to 2 and the inner integral goes from 2-x to 2? because I got the same but still get a negative result

anonymous · Answer

did you get -8/3  ?

anonymous · Answer

yes

anonymous · Answer

then , you sir are correct

anonymous · Answer

but is this a realistic result...I mean after all it's a negative volume

anonymous · Answer

this is what we call as signed volume, yes that makes no sense.

Remember in calc 2, we we integrate area under the x axis we get negative area; this is same thing

anonymous · Answer

ok, I think I understand it...plus I actually got my math right, so that's good....thanks a lot