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HMMT 二月 2002 · CALC 赛 · 第 4 题

HMMT February 2002 — CALC Round — Problem 4

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. Find the area of the region in the first quadrant x > 0 , y > 0 bounded above the graph of y = arcsin( x ) and below the graph of the y = arccos( x ).
解析
  1. Find the area of the region in the first quadrant x > 0 , y > 0 bounded above the graph of y = arcsin( x ) and below the graph of the y = arccos( x ). π/ 4 ∫ Solution: We can integrate over y rather than x . In particular, the solution is sin y d y + 0 π/ 2 ( ) ∫ √ 1 √ cos y d y = 1 − 2 = 2 − 2 . 2 π/ 4