不用计算,利用二重积分的性质判断下列重积分的符号:
(1)I=∫∫Dy2xe-xydσ,其中D:0≤x≤1,-1≤y≤0;
(2)I=∫∫Dln(1-x2-y2)dσ,其中D:x2+y2≤1/4.
(1)∵y2xe-xy﹥0.当0≤x≤1,-l≤y≤0 ∴I=∫∫Dy2xe-xydσ﹥0 (2)∵ln(1-x2-y2)<0,当x2+y2≤1/4时 ∴I=∫∫Dln(1-x2-y2)dσ﹤0
不用计算,利用二重积分的性质判断下列重积分的符号:
(1)I=∫∫Dy2xe-xydσ,其中D:0≤x≤1,-1≤y≤0;
(2)I=∫∫Dln(1-x2-y2)dσ,其中D:x2+y2≤1/4.
(1)∵y2xe-xy﹥0.当0≤x≤1,-l≤y≤0 ∴I=∫∫Dy2xe-xydσ﹥0 (2)∵ln(1-x2-y2)<0,当x2+y2≤1/4时 ∴I=∫∫Dln(1-x2-y2)dσ﹤0