求定积分：∫上3下2 {(1-x)/x^2}dx

题目

求定积分：∫上3下2 {(1-x)/x^2}dx

答案

∫(2~3) (1 - x)/x² dx
= ∫(2~3) (1/x² - 1/x) dx
= - 1/x - lnx |(2~3)
= (- 1/3 - ln3) - (- 1/2 - ln2)
= ln(2/3) + 1/6