Evaluate ∫y=0^{1}∫x=y^{2√2-y^{2}}y/2√x^{2}+y^{2}dxdy ,by clange the order of integration.

"\u222b_{y=0}^{1}\u222b_{x=y}^{2\\sqrt{2-y^{2}}} \\frac{y}{2}\\sqrt{x^{2}+y^{2}}dxdy\\\\\n\u222b_{x=0}^{1}\u222b_{y=x}^{\\sqrt{2-\\frac{x^2}{4}}} \\frac{y}{2}\\sqrt{x^{2}+y^{2}}dydx\\\\\n=\\int _0^1\\left(\\frac{\\left(3x^2+8\\right)^{\\frac{3}{2}}}{48}-\\frac{\\sqrt{2}x^3}{3}\\right)dx\\\\\n=\\frac{-48\\sqrt{3}\\ln \\left(2\\right)+32\\sqrt{3}\\ln \\left(\\sqrt{3}+\\sqrt{11}\\right)+23\\sqrt{11}}{192}-\\frac{1}{6\\sqrt{2}}\\\\\n=0.44671"

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