对于第1题，区域D由y=x²和y=√x围成。两条曲线交点为(0,0)和(1,1)。选择先对y后对x积分，x从0到1，y从x²到√x。

∫_{x=0}^{1} ∫_{y=x²}^{√x} x √y dy dx = ∫_{0}^{1} x [ (2/3) y^(3/2) ]_{y=x²}^{√x} dx = ∫_{0}^{1} x * (2/3)( x^(3/4) - x³ ) dx = (2/3) ∫_{0}^{1} ( x^(7/4) - x⁴ ) dx = (2/3)[ (4/11)x^(11/4) - (1/5)x⁵ ]_{0}^{1} = (2/3)(4/11 - 1/5) = (2/3)(20/55 - 11/55) = (2/3)*(9/55) = 6/55。

第2题区域D是以原点为圆心、半径为1的圆盘。被积函数为1/√(x²+y²)，适合用极坐标变换：x=r cosθ, y=r sinθ, dxdy = r dr dθ，r从0到1，θ从0到2π。

∬_D 1/√(x²+y²) dxdy = ∫_{θ=0}^{2π} ∫_{r=0}^{1} (1/r) * r dr dθ = ∫_{0}^{2π} dθ ∫_{0}^{1} dr = 2π * 1 = 2π。