計算二重積分∫∫xcos(x+y)dσ ,D是頂點分別為（0,0）,（π,0）和（π,π）的三角形閉區(qū)域
計算二重積分xcos(x+y)dσ ,其中D是頂點分別為(0,0),(π,0)和(π,π)的三角形閉區(qū)域.
∬xcos(x+y)dxdy=[0,π]∫xdx∫[0,x]cos(x+y)d(x+y)=[0,π]∫xdx[sin(x+y)]︱[0,x]
=[0,π]∫x(sin2x-sinx)dx=[0,π][∫xsin2xdx-∫xsinxdx]=[0,π][-(1/2)∫xd(cos2x)+∫xd(cosx)]
=[0,π]{-(1/2)[xcos2x-∫cos2xdx]+[xcosx-∫cosxdx]}
=[0,π]{-(1/2)[xcos2x-(1/2)sin2x]+[xcosx-sinx]}
=[0,π]{-(1/2)xcos2x+(1/4)sin2x+xcosx-sinx}
=-(1/2)π-π=-(3/2)π
我的問題是[0,π][-(1/2)∫xd(cos2x)+∫xd(cosx)]
=[0,π]{-(1/2)[xcos2x-∫cos2xdx]+[xcosx-∫cosxdx]}這一步是怎么來的?