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167

Part of 2006 Today's Calculation Of Integral

Problems(1)

Today's calculation of Integral 167

Source: Tokyo University entrance exam/Science 1982

11/11/2006
In xyzxyz plane find the volume of the solid formed by the points (x, y, z)(x,\ y,\ z) satisfying the following system of inequalities. 0≤z≤1+x+y−3(x−y)y, 0≤y≤1, y≤x≤y+1.0\leq z\leq 1+x+y-3(x-y)y,\ 0\leq y\leq 1,\ y\leq x\leq y+1.
calculusintegrationinequalitiesalgebrafunctiondomaingeometry