问题描述: 定积分∫(上限π/3,下限π/4)x/(sin^2x)dx 答案(1/4-√3/9)π+1/2ln2/3 1个回答 分类:数学 2014-10-13 问题解答: 我来补答 ∫(π/4→π/3) x/sin²x dx= ∫(π/4→π/3) xcsc²x dx= ∫(π/4→π/3) x d(- cotx)= - xcotx + ∫(π/4→π/3) cotx dx= - xcotx + ∫(π/4→π/3) 1/sinx d(sinx)= - xcotx + ln(sinx) |(π/4→π/3)= (- π/3)cot(π/3) + ln(sin(π/3)) - [(- π/4)cot(π/4) + ln(sin(π/4))]= (1/36)(9 - 4√3)π + (1/2)ln(3/2) ≈ 0.383531我的答案是对的,验算如下. 展开全文阅读