Question

计算定积分∫x xsinxdx/2 写出计算过程

计算定积分π到0 ∫xsinxdx/2 写出计算过程

Answer 1

∫x xsinxdx/2
=-1/2∫x^2dcosx
=-1/2[x^2cosx-∫cosxdx^2]
=-1/2x^2cosx+∫xcosxdx
=-1/2x^2cosx+∫xdsinx
=-1/2x^2cosx+xsinx-∫sinxdx
=-1/2x^2cosx+xsinx+cosx+c

追问

计算定积分π到0 ∫xsinxdx/2 写出计算过程 不好意思题目没写完整，麻烦给可以再写哈

追答

哈!这还要求助?
∫x xsinxdx/2
=-1/2∫x^2dcosx
=-1/2[x^2cosx-∫cosxdx^2]
=-1/2x^2cosx+∫xcosxdx
=-1/2x^2cosx+∫xdsinx
=-1/2x^2cosx+xsinx-∫sinxdx
=-1/2x^2cosx+xsinx+cosx+c
∫x xsinxdx/2 π到0 (不知道是0到π,还是π到0)
如果是π到0
[π到0] (-1/2x^2cosx+xsinx+cosx)=0+0+1-(1/2π^2+0-1)=1-1/2π^2+1=2-1/2π^2

追问

计算定积分π到0 ∫sinxdx/2 写出计算过程 π在上面，0在下面，不好写出来，那这题呢，谢谢，题目有点小变

追答

[0到π] (-1/2x^2cosx+xsinx+cosx)=(1/2π^2+0-1)-(0+0+1)=1/2π^2-2

Answer 2

慢慢写