Significant Figures

For x≤0
f(x)=0∫2​et−xdt=e−x(e²−1)
For 0f(x)=0∫x​ex−tdt+∫x²​et−xdt=ex+e²−x−2
For x≥2
f(x)=0∫2​ex−tdt=ex−2(e²−1)
For x≤0,f(x) is ↓ and x≥2,f(x) is ↑
∴ Minimum value of f(x) lies in x∈(0,2)
Applying A.M≥G.M,
minimum value of f(x) is 2(e−1)