Two points P and Q are chosen randomly, one on each of two adjacent sides of a

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Two points P and Q are chosen randomly, one on each of two adjacent sides of a unit square (see figure). What is the probability that the area of the triangle formed by the sides of the square and the line segment PQ is less than one-fourth the area of the square? Begin by showing that x and y must satisfy xy < 1/2 in order for the area condition to be met. Then argue that the required probability isdx 2x 1/2 and evaluate
the integral.

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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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