Let \(a\) be a positive real numbers such that \({\int }_{0}^{a}{e}^{x-[x]}dx=10e-9\) where [x] is the greatest integer …

Let \(a\) be a positive real numbers such that

\({\int }_{0}^{a}{e}^{x-[x]}dx=10e-9\)

where [x] is the greatest integer less than or equal to x. Then \(a\) is equal to :

[JEE Main 2021, 20 Jul (Shift 1)]