MathDB
Miklos Schweitzer 1962_7

Source:

September 18, 2008
functionintegrationtrigonometrycalculusreal analysisreal analysis unsolved

Problem Statement

Prove that the function f(ν)=∫11νdx(x2−1)(1−ν2x2) f(\nu)= \int_1^{\frac{1}{\nu}} \frac{dx}{\sqrt{(x^2-1)(1-\nu^2x^2)}} (where the positive value of the square root is taken) is monotonically decreasing in the interval 0<ν<1 0<\nu<1. [P. Turan]
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