Area of bounded region: int int [D] [2 - 3x + 4y] dA

[jman2807]

Use symmetry to evaluate the following where D is the region bounded by the square with vertices (+-5, 0) and (0, +-5).



I tried integrating as a type 2 using -x+5 and x+5 as bounds and multiplying by two. I even broke it in to four seperate integrals and still didnt come up with the right answer. Help appreciated. Thanks in advance.

 

[galactus]

I may have well give it a go. If it's not right, it'll be wrong, I suppose.

I would think a type II region would be:


\(\displaystyle \L\\2\int_{0}^{5}\int_{y-5}^{5-y}(2-3x+4y)dxdy=\frac{1300}{3}\)

Is that what you're aiming for or did I drop the ball.

 

[jman2807]

I tried that answer and it was a no go... I'm not sure what it means by symmetry... Anyway the assignment is now past due so no need to worry about it now. Thanks for trying.