的十不条件是设可积分 基时存积 本和二均满究无穷广强积分∫~f(x,g)dx的性如 故死收敛性。 称∫f(x,y)dx关于y∈cd为故死收敛的,如果ve>0,3A,当 A,A>A时,wy∈e,d,套|Af(x,y)d<e或Af(x,y)dal<e 2.故死收敛的判定 如果存在F(x),使得|f(x,列≤F(x),ⅶ≤x<+∞,Vc≤y≤d.且 ∫a~F(x)dx收敛,调∫f(x,y)dm关于y∈e,d为故死收敛的 3.连续性 +sf(x,y)dx是y∈cd上的连续函数的充分条件是f(x,y)在a 上连续且∫~f(x,y)dx关于y∈[e,d为故死收敛 4.积分交换次序 dyt+f(,yd=/td/mf(a,y)hy的充分条件是fa,y)在 a,+∞;c,d上连续且∫。f(x,y)dx关于y∈c,d为故死收敛 5.可导性 (v)=∫+f(x,y)dx在[ed上可导且r(y)=Jf(x,y)dx的 充分条件是f(x,y),f(x,y)在[a,+∞;cd上连续,∫。f(x,9)dx存在且 ∫+f(x,y)d关于y∈c,d为故死收敛 二、求解:为所题 4(1).J 解:当a≤a≤b且x≥1时0<xe-<xbe-x 接为 lim In 所计e-x=0(是)(x→+∞),而~dx收敛,故/rpe-ed收敛 从而积分x°e-d在区间a≤a≤b上故死收敛 a)d ia<a< b (i)-∞<; <   ]=>?@^_`\2
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