问题描述: 计算:定积分∫(在上1 ,在下√2/2 )(√1-X^2)/x^2 dx求详细过程答案,拜托大神... 1个回答 分类: 数学 2014-12-06 问题解答: 我来补答 令x=sint,则dx=cost dt∫(√2/2→1)√(1-x²)/x²dx=∫(π/4→π/2)cost/sin²t·costdt=∫(π/4→π/2)cos²t/sin²t dt=∫(π/4→π/2)cot²t dt=∫(π/4→π/2)(csc²t-1) dt=(-cot²t-t)|(π/4→π/2)=-π/2-(-1-π/4)=1-π/4 展开全文阅读