Question

∫(0,π/3)xcos3xdx=？请帮我看下解题过程对吗

∫(0,π/3)xcos3xdx=？请帮我看下解题过程对吗如果有错误请指出并解释原因，谢谢

Answer 1

不对，答案是-2/9

第七行应该是 π/9*（sinπ-sin0）+1/9*(cosπ-cos0)
最后的答案是-2/9才对

Answer 2

∫(0->π/3) xcos3x dx
=(1/3)∫(0->π/3) x dsin3x
=(1/3)[ x.sin3x]|(0->π/3) - (1/3)∫(0->π/3) sin3x dx
=0 + (1/9)[ cos3x]|(0->π/3)
=-2/9

追问

没看懂

追答

∫(0->π/3) xcos3x dx
/ (1/3)dsin3x = cos3x dx
=(1/3)∫(0->π/3) x dsin3x
/ 分部积分 ∫ udv = uv - ∫ v du , u= x , v= sin3x
=(1/3)[ x.sin3x]|(0->π/3) - (1/3)∫(0->π/3) sin3x dx

=0 + (1/9)[ cos3x]|(0->π/3)
=-2/9