MathDB

15

Part of 2007 Stanford Mathematics Tournament

Problems(2)

SMT 2007 Team #15

Source:

6/30/2012
Evaluate ∫0∞tan⁡−1(πx)−tan⁡−1xxdx\int_{0}^{\infty}\frac{\tan^{-1}(\pi x)-\tan^{-1}x}{x}dx
integrationtrigonometrylogarithms
Probability that x Exceeds y

Source:

3/15/2010
A number x x is uniformly chosen on the interval [0,1] [0,1], and y y is uniformly randomly chosen on [\minus{}1,1]. Find the probability that x>y x>y.
probabilityanalytic geometrygeometryrectangle