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The value of $\int_{-\infty}^{+\infty} e^{-t} \delta (2t-2){d}t$, where $\delta (t)$ is the Dirac delta function, is

  1. $\frac{1}{2e}$
  2. $\frac{2}{e}$
  3. $\frac{1}{e^{2}}$
  4. $\frac{1}{2e^{2}}$
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