Question

设x≤0时,f(x)=1+x^2,x＞0时,f(x)=e^(-x),求∫(1,3)f(x-2)dx

Answer 1

简单计算一下即可，答案如图所示

Answer 2

∫(1,3)f(x-2)dx
=∫(-1,1)f(x)dx
=∫(-1,0)f(x)dx+∫(0,1)f(x)dx
=∫(-1,0)1+x^2dx+∫(0,1)e^(-x)dx
=x+x^3/3|(-1,0)-e^(-x)|(0,1)
=0-(-1-1/3)-1/e+1
=7/3-1/e