证明√2×e^-½≦∫(-1／√2,1/√2)e^-x^2dx≦√2定积分这的题

Question

证明√2×e^-½≦∫(-1／√2,1/√2)e^-x^2dx≦√2
定积分这的题

Answer 1

由被积函数为偶函数,∫(-1／√2,1/√2)e^-x^2dx=2∫(0,1/√2)e^-x^2dx.
[e^-x^2]'<0,被积函数单减,于是:
e^-½<=e^-x^2<=1,积分即可