Question

定积分 题目

定积分 题目解题过程要详细！

Answer 1

(1)
∫cotx dx
=∫(cosx/sinx) dx
=∫(1/sinx)d(sinx)
=ln|sinx| |(π/4，0)
x=0为积分的瑕点
=ln(√2/2) - (-∞)
=+∞，该积分发散
(2)
∫tanxdx
=∫(sinx/cosx)dx
=∫-1/cosx d(cosx)
=-ln|cosx| |(π/4，0)
=- [ln(√2/2) - ln1]
=-ln(√2/2)
(3)
∫(sinx+cosx) dx
=-cosx + sinx |(π/2，0)
=0 + 1 - (-1+0)
=2