HMMT 二月 2000 · CALC 赛 · 第 8 题
HMMT February 2000 — CALC Round — Problem 8
题目详情
- Find ln sin d . 0 v s u r q u p t 0
解析
- Let I denote the giv en in tegral. Under the transformation ! , I transforms to 2 R 2 ln ( os( )) d . So, 0 R 2 2 I = ln (sin os ) d 0 R = (ln (sin 2 ) ln 2) d (2 ) = 2 0 R 1 = + sin( ) d giving I = ln 2 . 0 2 ln 2 2 2 R pi 2 = ln 2 + sin( ) d 0 2 pi = ln 2 + I 2 2 2 2