求二重积分∫∫xcos(x+y)dσ,其中D是顶点分别为(0,0),(π,0),(π...答:∫[0,π]∫[0,x]xcos(x+y)dydx =∫[0,π]xsin(x+y)[0,x]dx =∫[0,π]x(sin2x-sinx)dx =∫[0,π]xsin2xdx-∫[0,π]xsinxdx =-1/2∫[0,π]xdcos2x+∫[0,π]xdcosx =-1/2xcos2x[0,π]+1/2∫[0,π]cos2xdx+xcosx[0,π]-∫[0,π]cosxdx =-π/2+1...
求二重积分∫∫xcos(x+y)dσ,其中D是顶点分别为(0,0),(0,π)和(π...答:改成你的条件后,∫[0,π]∫[0,x]xcos(x+y)dydx =∫[0,π]xsin(x+y)[0,x]dx =∫[0,π]x(sin2x-sinx)dx =∫[0,π]xsin2xdx-∫[0,π]xsinxdx =-1/2∫[0,π]xdcos2x+∫[0,π]xdcosx =-1/2xcos2x[0,π]+1/2∫[0,π]cos2xdx+xcosx[0,π]-∫[0,π]...