how can greens theorem be verified for the region R defined by $\displaystyle (x^2 + y^2 \leq 1), (x + y \geq 0), (x - y \geq 0)$ .... P(x,y) = xy, Q(x,y) = $\displaystyle x^2$

> okay i know $\displaystyle \int_C Pdx + Qdy = \int\int \left(\frac{dQ}{dx} - \frac{dp}{dy}\right) dA$

so: $\displaystyle \int_C xy dx + x^2dy = \int\int_D \left(2x - x\right) dy dx$

but i can't figure out the limits for the double integral: $\displaystyle \int\int_D \left(2x - x\right) dy $... I know they can be found by those inequalities but i'm reachin a dead end.. any suggestions and working out please?

also what is the region of integration for the left hand side please?