定积分½π到π(sinx+1/x)dx

定积分½π到π(sinx+1/x)dx
定积分½π到π(sinx+1/x)dx

定积分½π到π(sinx+1/x)dx
∫(π/2→π) (sinx + 1/x) dx
= [- cosx + ln|x|] |(π/2→π)
= [- cosπ + ln(π)] - [- cos(π/2) + ln(π/2)]
= 1 + ln(π) - 0 - [ln(π) - ln(2)]
= 1 + ln(2)