填空题1<D)0 \int _{-1}^{1}(\mid x \mid+x)e^{- \mid x \mid }dx=解原式= \int _{-1}^{0}(-x+x)e^{x}dx+\int _{0}^{1}(x+x)e^{-x}dx= \int _{0}^{1}2xe^{-x}dx= \int _{0}^{1}2x(-e^{-x})'dx=(-2xe^{-x})\mid _{0}^{1}+2 \int _{0}^{1}e^{-x}dx=-2e^{-1}+2(-e^{-x})\mid=2(1-2e^{-1}).1<11.设函数f(x+\frac {1}{x})= \frac {x+x^{3} 计算题1<D)设某商品从时刻0到时刻t的销售量为x(t)=kt,t \in [0,T],k>0..欲在T时将数量为A的商品销售完,试求:(1)t时的商品剩余量,并确定k的值;(2)在时间段[0,7]上的平均剩余量.解(1)t时的商品剩余量y(t)=A-x(t)=A-kt由y(T)=0得k=A/T(2)\overline {y(t)}= \frac {1}{T} \int _{0}^{t}y(t)dt100_100设函数f(x)具有连续的一阶导数,且满足f(x)= \int _{0}^{x}(x^{2}-t^{2})f'(t)dt+x^{2}求f(x)的表达式.解f(x)=x^{2} \int