MathDB
Today's calculation of integral 100

Source: created by kunny

March 30, 2006
calculusintegrationinequalitiesfunctionlimitcalculus computations

Problem Statement

Let a,b,ca,b,c be positive numbers such that abc=116.abc=\frac{1}{16}. Prove the following inequality. ∫0∞x2(x2+a2)(x2+b2)(x2+c2) dx≤π. \int_0^{\infty} \frac{x^2}{(x^2+a^2)(x^2+b^2)(x^2+c^2)}\ dx\leq \pi.
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