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HMMT 二月 2010 · GEN2 赛 · 第 4 题

HMMT February 2010 — GEN2 Round — Problem 4

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 4 ] For 0 ≤ y ≤ 2, let D be the half-disk of diameter 2 with one vertex at (0 , y ), the other vertex on y the positive x -axis, and the curved boundary further from the origin than the straight boundary. Find the area of the union of D for all 0 ≤ y ≤ 2. y
解析
  1. [ 4 ] For 0 ≤ y ≤ 2, let D be the half-disk of diameter 2 with one vertex at (0 , y ), the other vertex on y the positive x -axis, and the curved boundary further from the origin than the straight boundary. Find the area of the union of D for all 0 ≤ y ≤ 2. y Answer: π 2