定积分问题,图上这个是怎么算出来的?请给出具体步骤。
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∫(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
=∫(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
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