Double Integral $\iint_D\ (x+2y)\ dxdy$ $$\iint_D (x+2y)\ dxdy $$
If the area is range by $x=2,\ x=3,\ y=x,\ y=2x$,
how to include the lines?  How limits for integral will looks like?
You mean something like this? ( I made mess)
$$\iint_D (x+2y)\ dxdy $$
If the area is range by $x=2,\ x=3,\ y=x,\ y=2x$,
how to include the lines?  How limits for integral will looks like?
So
$$ \int_{y=x}^{2x}\ (x+2y)\ dx =   \int_{y=x}^{2x} x dx + \int_{y=x}^{2x}\  2y dx = \frac{1}2 [x^{2}] + 2y \int_{y=x}^{2x}\  1 dx = \frac{1}{2}(2x)^{2}-y^{2} + 2y(2x-y)  $$
and
$$  \int_{x=2}^3 [ \frac{1}{2}(2x)^{2}-y^{2} + 2y(2x-y) ]dy = \frac{1}{2}\int_{x=2}^3 (2x)^{2}  dy - \int_{x=2}^3 y^{2} dy + \int_{x=2}^3 4xy dy - \int_{x=2}^3 2y^{2}  dy = \frac{1}{2} (2x)^{2} \int_{x=2}^3  1 dy - [\ \frac{1}{3}y^{3}] + 4x[\frac{1}{2}y^{2}] - 2[\frac{1}{3}y^{3}]= \frac{1}{2} (2x)^{2}... $$ and I do not know.  

Hint :
$$
\iint_D\ (x+2y)\ dx\,dy=\int_{x=2}^3\int_{y=x}^{2x}\ (x+2y)\ dx\,dy.
$$
