Evaluate the integral: $\iint_D xydA$ where D is union of the two regions
The integral is given as :
$\int\limits_{-1}^{1}\int\limits_{0}^{\sqrt{1-x^2}}xydydx+\int\limits_{-\sqrt3}^0 \int\limits^{\sqrt{1+y^2}}_{-y\sqrt3-1}xy\, dx\,dy $
But what I don't understand is in the first integral , $x$ varies from $-1$ to $1$ and this should imply $y$ varies from $0$ to $1$
Similarly in the second integral, $y$ varies from $0$ to $-\sqrt{3}$ implies $x$ varies from $-1$ to $2$
Yet they are not put as limits in the integration? Why is it so?