Let \(a\) be a positive real numbers such that \(\int_0^a e^{x-[x]} d x=10 e-9\), where \([x]\) is the greatest integer …

Let \(a\) be a positive real numbers such that \(\int_0^a e^{x-[x]} d x=10 e-9\), where \([x]\) is the greatest integer less than or equal to \(x\). Then \(a\) is equal to:

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