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Today's calculation of Integral 398

Source: 2007 Hokkaido University entrance exam/Science, 2nd Round

January 3, 2009
calculusintegrationinequalitiesgeometrysearchcalculus computations

Problem Statement

In xyz xyz space, find the volume of the solid expressed by the sytem of inequality: 0≦x≦1, 0≦y≦1, 0≦z≦1 0\leqq x\leqq 1,\ 0\leqq y\leqq 1,\ 0\leqq z\leqq 1 x^2 \plus{} y^2 \plus{} z^2 \minus{} 2xy \minus{} 1\geqq 0
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