HMMT 二月 2002 · CALC 赛 · 第 4 题
HMMT February 2002 — CALC Round — Problem 4
题目详情
英文原题
- Find the area of the region in the first quadrant x > 0 , y > 0 bounded above the graphof y = arcsin( x ) and below the graph of the y = arccos( x ).
解析
英文解析
- Find the area of the region in the first quadrant x > 0 , y > 0 bounded above thegraph 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 +
π/ 2 ( )0
∫ √
√1
cos y d y = 1 − 2 = 2 − 2 .
π/ 42