Question

计算二重积分(y-z)x^2dzdx+(x+y)dxdy其中是柱面x^2+y^2=1及平面z=0 z=3所围成

Answer 1

简单分析一下，详情如图所示

Answer 2

=∫x（yzx^2-1/2(xz)^2）dx+∫y（1/2x^2+xy）dy=[1/3yzx^3-1/6z^2x^3+1/2x^2y+1/2xy^2] |z[0,2]、y[0,1]、x[0,1]=1