help me to get started.$\displaystyle \int_D \int (2x-y) dA$
D is bounded by the circle with center the origin and radius 2.
When dealing with circles, I would suggest converting to polar coordinates.
Do you know the following formulae:
$\displaystyle x = r \cos (\theta) $
$\displaystyle y = r \sin (\theta) $
Also, do you know the Jacobian matrix for a change of variables in double integration?
Once you have converted to polar coordinates, your variables of integration will be r, the radius, and $\displaystyle \theta$, the angle. Clearly, the limits for these are as follows:
$\displaystyle 0 \leq r \leq 2 $
$\displaystyle 0 \leq \theta \leq 2\pi $