定积分π⼀3到π⼀4 x⼀sin^2x dx

2025-03-10 13:17:20
推荐回答(2个)
回答1:

∫(π/3 to π/4) x/sinx dx =∫(π/3 to π/4) xcscx dx =∫(π/3 to π/4) x d(-cotx) =-xcotx(π/3 to π/4) + ∫(π/3 to π/4) cotx dx,分部积分法 =π/(3√3)-π/4 + ln|sin|(π/3 to π/4) =π/(3√3)-π/4 - (1/2)ln(3/2)

回答2:

用分部积分法,x*csc方x+定积分π/4到π/3(csc方x)dx