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Today's calculation of Integral 79

Source: 1980 Shimane University Entrance Exam

September 8, 2005
calculusintegrationgeometryalgebrafunctiondomainfactorial

Problem Statement

Find the area of the domain expressed by the following system inequalities. x≥0, y≥0, x1p+y1p≤1 (p=1,2,⋯ )x\geq 0,\ y\geq 0,\ x^{\frac{1}{p}}+y^{\frac{1}{p}} \leq 1\ (p=1,2,\cdots)
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