MathDB
Today's calculation of Integral 591

Source: created by kunny

March 29, 2010
calculusintegrationinequalitiescalculus computations

Problem Statement

Let a, b, c a,\ b,\ c be real numbers such that a≥b≥c≥1 a\geq b\geq c\geq 1. Prove the following inequality: \int_0^1 \{(1\minus{}ax)^3\plus{}(1\minus{}bx)^3\plus{}(1\minus{}cx)^3\minus{}3x\}\ dx\geq ab\plus{}bc\plus{}ca\minus{}\frac 32(a\plus{}b\plus{}c)\minus{}\frac 34abc.
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