Just E

Calculus Level 4

Let \(f(x) = \begin{cases} 20 \quad &, \quad x = 1 \\ \dfrac{x^{20}-1}{x-1} \quad &,\quad \text{otherwise} \end{cases} \).

And let \(\displaystyle y = \int_0^\infty f(x) e^{-x} \, dx \).

Compute \(99 + (\lfloor y \rfloor \bmod{100} ) \).

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