7

Part of 1962 Miklós Schweitzer

Problems(1)

Miklos Schweitzer 1962_7

Source:

Prove that the function

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<\nu<1

functionintegrationtrigonometrycalculusreal analysisreal analysis unsolved