设f(x)=e^|x|,则∫ -2,2 F(X)dx=?

f(x)=e^|x|
∫f(x)dx=∫e^|x|dx
Method1:
f(-x)=e^|-x|=e^|x|=f(x)
∴f(x)为偶函数
∫e^|x|dx
=2∫(e^x)dx
=2(e^x)
=2(e²-e^0)
=2(e²-1)
Method2:
∫e^|x|dx,分段函数,将e^|x|分为e^(-x)和e^x情况讨论
=∫e^xdx+∫e^(-x)dx
=e^x-[e^(-x)]
=e²-e^0-[e^0-e^-(-2)]
=e²-1-[1-e²]
=2e²-2
=2(e²-1)