Evaluate after changing the order of integration $$\int_1^{1/4}\int_{\sqrt{x-x^2}}^{\sqrt{x}}\left(\dfrac{x^2-y^2}{x^2}\right)dydx$$ I have done the change of order of integration and it comes out to be $$=\int_{\sqrt{3}/4}^{1/2}\int_{1/4}^{1/2~-\sqrt{1/4~-y^2}}\left(\dfrac{x^2-y^2}{x^2}\right)d...