18

Part of 2015 BMT Spring

Problems(2)

2015 BMT Team 18

Source:

x \in [0, 1]

is selected uniformly at random. A point

(a, b)

is called friendly to

x

if there exists a circle between the lines

y = 0

y = 1

that contains both

(a, b)

(0, x)

. Find the area of the region of the plane determined by possible locations of friendly points.

BMT 2015 Spring - Individual 18

Source:

\sum_{n=1}^{\infty}\frac{1}{(2n - 1)(3n - 1)}