定积分问题,图上这个是怎么算出来的?请给出具体步骤。

2025-04-07 07:16:43
推荐回答(1个)
回答1:

∫(0->x) (x-u)sinudu
=∫(0->x)xsinudu -∫(0->x)usinudu
=x∫(0->x)sinudu +∫(0->x)udcosu
=-x∫(0->x)dcosu +ucosu|(0->x) -∫(0->x)cosudu
=-xcosu|(0->x)+(xcosx-0cos0)-sinu|(0->x)
=-(xcosx-xcos0)+xcosx-(sinx-sin0)
=-xcosx+x+xcosx+sinx
=x-sinx