Question

二重积分,求由z=xy,x+y=1,x=0,y=0所围空间区域的体积

Answer 1

作二重积分ʃʃ(xy)dx dy,积分范围d为x+y=1,x=0,y=0所为区域

ʃʃ(xy)dx dy=ʃ [积分范围0->1]dx ʃ [积分范围0->1-x](xy) dy

=ʃ [0->1](1/2)x(1-x)^2 dx

=1/24