# Limit of a Definite Integral 3

Calculus Level 5

$\large \lim_{n\to\infty} \int_0^{n\pi} e^{-x} |\sin(x)| \, dx$

If the limit above can be expressed as $$\alpha \left( \frac{1+e^\beta}{1-e^\lambda} \right)$$ where $$\alpha, \beta, \lambda$$ are real numbers, $$\alpha \geq 0$$ and $$\beta, \lambda \leq 0$$ and $$n$$ is an integer, find the value of $$2(\alpha+\beta-\lambda)$$.

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