定积分∫0到π √[sin^3(x)-sin^5(x)]dx

2025-06-29 09:51:58
推荐回答(1个)
回答1:

∫0到π √[sin^3(x)-sin^5(x)]dx
=∫0到π √sin^3(x)[1-sin^2(x)]dx
=∫0到π √sin^3(x)cos^2(x)dx
=∫0到π cos(x)√sin^3(x)dx
=∫0到πsin^3/2(x)dsin(x)
=2/5sin^5/2(x)│0到π
=0