求定积分,
来源：学生作业帮助网 编辑：六六作业网 时间：2024/11/16 07:53:52
求定积分,求定积分,求定积分,因为x^3(cosx)^2是个奇函数,所以∫(-π/2->π/2)x^3(cosx)^2dx=0所以原积分=∫(-π/2->π/2)(sinx)^2(cosx)^2dx=
求定积分,
求定积分,
求定积分,
因为x^3(cosx)^2是个奇函数,所以∫(-π/2->π/2) x^3(cosx)^2dx=0
所以原积分=∫(-π/2->π/2) (sinx)^2(cosx)^2dx=(1/4)∫(-π/2->π/2) (sin2x)^2dx
=(1/4)∫(0->π/2) (sin2x)^2d(2x)
=(1/4)∫(0->π) (sinu)^2du
=(1/2)∫(0->π/2) (sinu)^2du
=π/8