f(x) =∫(0->x^2) (2-t)e^(-t) dt
f'(x) =2x.(2-x^2)e^(-x^2)
f'(x) =0
x=0 or √2 or -√2
f'(x)|x=0+ >0, f'(x)|x=0- <0
x=0 (min)
f'(x)|x=√2+ <0, f'(x)|x=√2- >0
x=√2 (max)
f'(x)|x=-√2+ <0, f'(x)|x=√2- >0
x=-√2 (max)
最大值 = f(√2) or f(-√2)
最大值
=∫(0->2) (2-t)e^(-t) dt
=-∫(0->2) (2-t) de^(-t)
=-[ (2-t).e^(-t) ]|(0->2) - ∫(0->2) e^(-t) dt
=2 +[e^(-t)]|(0->2)
=2 +e^(-2) -1
=1+e^(-2)
最小值 = f(0) =0
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