Solución

D(x2y2)dA=11y411y4(x2y2)dxdy=4644095\iint_D\big(x^2-y^2\big)dA = \int_{-1}^1\int_{y^4-1}^{1-y^4}\big(x^2-y^2\big)dxdy = \frac{464}{4095}