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Today's calculation of Integral 797

Source: 2012 Tokyo Institute of Technology entrance exam, problem 6

February 29, 2012
calculusintegrationgeometry3D geometrytetrahedrontrigonometrycalculus computations

Problem Statement

In the xyzxyz-space take four points P(0, 0, 2), A(0, 2, 0), B(3,−1, 0), C(−3,−1, 0)P(0,\ 0,\ 2),\ A(0,\ 2,\ 0),\ B(\sqrt{3},-1,\ 0),\ C(-\sqrt{3},-1,\ 0). Find the volume of the part satifying x2+y2≥1x^2+y^2\geq 1 in the tetrahedron PABCPABC.
50 points
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